Rotational Motion Part I


 Shonda Blake
 4 years ago
 Views:
Transcription
1 AP Physics Rotational Motion Part I Introduction: Which moves with greater speed on a merrygoround  a horse near the center or one near the outside? Your answer probably depends on whether you are considering the translational or rotational motion of the horses. Have you ever linked arms with friends at a skating rink while making a turn? If you have, you probably noticed that the person on the inside moved very little while the person on the outside had to run to keep up. The outside person traveled a greater distance per period of time and therefore had the greater translational speed. During the same period of time all skaters rotated through the same angle per period of time and had the same rotational speed. In our previous study of motion we discussed translational motion  that is the motion of bodies moving as a whole without regard to rotation. In this unit we will extend our ideas of motion to include the rotation of a rigid body about a fixed axis. If the axis is inside the body we tend to say the body rotates about its axis. If the axis is outside the body, we say the body revolves about an axis. An example of this would be the earth which daily rotates about its axis and yearly revolves around the sun. An object rotating about an axis tends to remain rotating about the same axis unless acted upon by a net external influence. This property of a body to resist changes in its rotational state is called rotational inertia. The rotational inertia of a body depends on the amount of mass the body possesses and on the distribution of that mass with respect to the axis of rotation. The greater the distance of the bulk of the mass from the axis of rotation  the greater the rotational inertia. A long pendulum has a greater rotational inertia than a short one. The period of a pendulum is directly proportional to the square root of the length of the pendulum. It takes more time to change the rotational inertia of a long pendulum as it swings back and forth. People and animals with long legs tend to walk with slower strides than those with short legs for the same reason. Have you ever tried running with your legs straight? Performance Objectives: Upon completion of the readings and activities of the unit and when asked to respond either orally or on a written test, you will be able to: state relationships between linear and angular variables. recognize that the rotational kinematics formulas are analogous to the translational ones. Use these formulas to solve problems involving rotating bodies. define rotational inertia or moment of inertia. Calculate the rotational inertia for a point mass, a system of point masses, and rigid bodies. use the parallel axis theorem to find the moment of inertia about an axis other than the center of mass. calculate the kinetic energy of a rotating body. define torque. Calculate the net torque acting on a body. state Newton s second law for rotation. Recognize that the rotational dynamics formulas are analogous to the translational ones. Use these formulas to solve problems involving rotating bodies. use the workkinetic energy theorem for rotation to solve problems. Textbook Reference: Tipler: Chapter 9 Glencoe Physics: Chapter 8 "To every thing  turn, turn, turn there is a season  turn, turn, turn and a time for every purpose under heaven."  The Byrds (with a little help from Ecclesiastes) Recall: From the definition of a radian (arc length/radius) θ = s/r, where s is the arc length, r is the radius and θ is the angle measure in radians. The following quantities are called the bridges between linear and angular measurements: s = rθ v = rω a T = rα a R = v 2 /r = rω 2 Definitions and Conversions: 1. What angle in radians is subtended by an arc 3.0 m in length, on the circumference of a circle whose radius is2.0 m? 1.5 rad 2. What angle in radians is subtended by an arc of length cm on the circumference of a circle of diameter cm? What is the angle in degrees? 1.57 rad The angle between two radii of a circle of radius 2.00 m is 0.60 rad. What length of arc is intercepted on the circumference of the circle by the two radii? 1.2 m 4. What is the angular velocity in radians per second of a flywheel spinning at the rate of 7230 revolutions per minute? 757 rad/sec
2 5. If a wheel spins with an angular velocity of 625 rad/s, what is its frequency in revolutions per minute? 5968 rpm 6. Compute the angular velocity in rad/s, of the crankshaft of an automobile engine that is rotating at 4800 rev/min. 503 rad/sec Rotational Kinematics: Rotational motion is described with kinematic formulas just like the translational motion formulas. To get the rotational kinematic formulas, substitute the rotational variables. 7. A flywheel accelerates uniformly from rest to an angular velocity of 94 radians per second in 6.0 seconds. What is the angular acceleration of the flywheel in radians per second squared? 16 rad/s 2 8. a) Calculate the angular acceleration in radians per second squared of a wheel that starts from rest and attains an angular velocity of 545 revolutions per minute in 1.00 minutes. b) What is the angular displacement in radians of the wheel during the first minutes? c) During the second minutes? 0.95 rad/s rad rad 9. Find the angular displacement in radians during the second 20.0 second interval of a wheel that accelerates from rest to 725 revolutions per minute in 1.50 minutes? 506 radians 10. A fly wheel requires 3.0 seconds to rotate through 234 rad. Its angular velocity at the end of this time is 108 rad/s. Find a) the angular velocity at the beginning of the 3 second interval; b) the constant angular acceleration. 48 rad/s 20.0 rad/s A playground merrygoround is pushed by a child. The angle the merrygoround turns through varies with time according to θ(t) = 2t t 3, where θ is in radians and t is in seconds. a) Calculate the angular velocity of the merrygoround as a function of time. ω = t 2 b) What is the initial value of the angular velocity? 2 rad/s c) Calculate the instantaneous velocity at t = 5.0 sec. d) Calculate the average angular velocity for the time interval t = 0 to t = 5 seconds rad/s 3.25 rad/s 12. A rigid object rotates with angular velocity that is given by ω = 4 + 8t 2, where ω is in rad/sec and t is in seconds. a) Calculate the angular acceleration as a function of time. b) Calculate the instantaneous angular acceleration a at t = 2 sec. c) Calculate the average angular acceleration for the time interval t = 0 to t = 2seconds. α = 16t 32 rad/s 2 16 rad/s A bicycle wheel of radius 0.33 m turns with angular acceleration α = t, where α is in rad/s 2 and t is in seconds. It is at rest at t = 0. a) Calculate the angular velocity and angular displacement as functions of time. b) Calculate the maximum positive angular velocity and maximum positive angular displacement of the wheel. ω = 1.2t  0.2t 2 θ = 0.6t t rad/s 7.2 rad 14. A roller in a printing press turns through an angle θ given by θ(t) = 2.50t t 3. a) Calculate the angular velocity of the roller as a function of time. ω(t) = 5t 1.2t 2 b) Calculate the angular acceleration of the roller as a function of time. α(t) = 5 2.4t c) What is the maximum positive angular velocity and at what value of t does it occur? 5.21 rad/s 2.08 sec 15. a) A cylinder 0.15 m in diameter rotates in a lathe at 750 rpm. What is the tangential velocity of a point on the surface of the cylinder? b) The proper tangential velocity for machining cast iron is about 0.60 m/s. At how many rpm should a piece of stock 0.05 m in diameter be rotated in a lathe? 5.89 m/s 229 rev/min 16. Find the required angular velocity of an ultracentrifuge in rpm for the radial acceleration of a point 1.00 cm from the axis to equal 300,000g (that is 300,000 times the acceleration of gravity) x 10 5 rev/min 17. A wheel rotates with a constant angular velocity of 10 rad/s. a) Compute the radial acceleration of a point 0.5 m from the axis using the relation, a = rω m/s 2 b) Find the tangential velocity of the point, and compute its radial acceleration from the relation, a c = v 2 /r. 5m/s 50 m/s 2 Rotational Inertia is the resistance of a rotating body to changes in its angular velocity. According to Newton's First Law a body tends to resist a change in its motion. The amount of inertia a body possesses is directly related to the mass. For rotational motion, an analogous situation exists. However, rotational inertia depends on the mass and on the distribution of the mass about the axis of rotation. This quantity that relates mass and position of the mass relative to the axis of rotation is called the moment of inertia and has units of kgm 2. The symbol for moment of inertia is I. For a point mass m a distance r from the axis of rotation, the moment of inertia will be I = mr 2. For bodies made up of several small masses just add all the moments of inertia together. For bodies which are not composed of discrete point masses but are continuous distributions of matter, the methods of calculus must be used to find the moment of inertia. The moments of inertia for a few simple but important rigid bodies of uniform composition are listed on Page 295 in Tipler Physics.
3 18. Small blocks, each of mass 2.0 kg, are clamped at the ends and at the center of a light rod 1.2 m long. Compute the moment of inertia of the system about an axis passing through a point onethird of the length from one end of the rod if the moment of inertia of the light rod can be neglected kgm Find the moment of inertia about each of the following axes for a rod that is 4.00 cm in diameter and 2.00 m long and has a mass of 8.00 kg. a) An axis perpendicular to the rod and passing through its center. b) An axis perpendicular to the rod and passing through one end. c) A longitudinal axis passing through the center of the rod kgm kgm kgm Four small spheres, each of mass kg, are arranged in a square m on a side and connected by light rods of negligible mass. Find the moment of inertia of the system about an axis a) perpendicular to the plane of the square through the center kgm 2 b) bisecting two opposite sides of the square kgm What is the rotational inertia of a solid ball 0.50 min radius that weighs 80.0 N if it is rotated about a diameter? kgm What is the rotational inertia of a thick ring that is rotating about an axis perpendicular to the plane of the ring passing through its center? The ring has a mass of 1.20 kg and a diameter of 45.0 cm. The hole in the ring is 15.0 cm wide kgm A wagon wheel is constructed as shown in the figure. The radius of the wheel is m and the rim has a mass of 1.20 kg. Each of the eight spokes, which lie along a diameter and are m long has a mass of kg. What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel? kgm 2
4 Parallel Axis Theorem: The moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction of space. The moment of inertia about any axis parallel to that axis through the center of mass is given by: Iparallel axis = Icom + Md 2 where I parallel axis is the moment of inertia about an new axis (parallel to the original axis of rotation), I com is the moment of inertia about the center of mass, M is the mass of the object and d is the distance between the original axis of rotation about the center of mass and the new proposed axis of rotation. 24. Use the parallel axis theorem to calculate the moment of inertia of a uniform thin rod of mass M and length l for an axis perpendicular to the rod at one end. Ml 2 /3 25. Use the parallel axis theorem to calculate the moment of inertia of a square sheet of metal of side length a and mass M for an axis perpendicular to the sheet and passing through one corner. 2Ma 2 /3 26. Find the moment of inertia of a thinwalled hollow cylinder of mass M and radius R about an axis perpendicular to its plane at an edge of the cylinder. 2MR A thin, rectangular sheet of steel is 0.30 m by 0.40 m and has a mass of 16.0 kg. Find the moment of inertia about an axis a) in the plane of the sheet, through the center, parallel to the long sides kgm 2 b) in the plane of the sheet, through the center, parallel to the short sides kgm 2 c) perpendicular to the sheet and through the center kgm A uniform, thin rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis through the center, perpendicular to the plane of the square. Ma 2 /3 29. Which pendulum has more rotational inertia, a long or short one? 30. The four objects shown in the figure below have equal masses m. Object A is a solid cylinder of radius R. Object B is a hollow, thin cylinder of radius R. Object C is a solid square whose length of side = 2R. Object D is the same size as C, but hollow (i.e., made up of four thin sticks). The objects have axes of rotation perpendicular to the page and through the center of gravity of each object. a) Which object has the smallest moment of inertia? b) Which object has the largest moment of inertia? Kinetic Energy of Rotation: Because a rotating rigid body consists of particles in motion, it has kinetic energy. This kinetic energy is computed using the moment of inertia of the body and the angular velocity. KE = ½Iω The rotor of an electric motor has a rotational inertia of 45 kgm 2. What is its kinetic energy if it turns at 1500 revolutions per minute? 555 kj 32. A grinding wheel in the shape of a solid disk is m in diameter and has a mass of 3.00 kg. The wheel is rotating at 3600 rev/min about an axis through its center. a) What is its kinetic energy? 1066 J b) How far would it have to drop in free fall to acquire the same kinetic energy? 36.3 m 33. The flywheel of a gasoline engine is required to give up J of kinetic energy while its angular speed decreases from 660 rev/min to 540 rev/min. What moment of inertia is required for the wheel? kgm A phonograph turntable has a kinetic energy of J when turning at 78 rpm. What is the moment of inertia of the turntable about the rotation axis? 35. Energy is to be stored in a large flywheel in the shape of a disk with radius of 1.20 m and a mass of 80.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 5000 m/s 2. What is the maximum kinetic energy that can be stored in the flywheel? 1.20 x 10 5 J 36. A light flexible rope is wrapped several times around a N solid cylinder with a radius of 0.25 m. The cylinder which can rotate without friction about a fixed horizontal axis is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 5.00 m. What must P be for the final speed of the end of the rope to be 4.00 m/s? 37. Two blocks, one of mass 4.0 kg and the other of mass 2.0 kg are connected by a light rope that passes over a pulley as shown in the figure to the right. The pulley has radius 0.20 m and moment of inertia 0.32 kgm 2. The rope does not slip on the pulley rim. The larger mass is 5.0 m above the floor and released from rest. Use energy methods to calculate the velocity of the 4kg block just before it strikes the floor m/s
5 Torque: To change the translational inertia of a body you have to apply a net external force. To change the rotational inertia of a body you have to apply a torque (rhymes with fork). If you studied torque in previous science courses it was probably defined as the product of the force and the length of the torque arm. The torque arm (sometimes called lever arm) is the perpendicular distance between the line of action of the force and the axis of rotation. In order to solve problems involving torque, you need to understand how torque is calculated and then be able to calculate the net torque acting on a body. 38. Calculate the torque (magnitude and direction) about point 0 due to the force F in each of the situations sketched in the figure. In each case the object to which the force is applied has length 4.00 m, and the force F =20.0 N. 41. A small ball of mass 0.75 kg is attached to one end of a 1.25 meter long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is30 from the vertical, what is the magnitude of the torque about the pivot? 4.6 mn 42. Find the net torque on the wheel in the figure about the axle through O if a = 10 cm and b = 25 cm mn cw 43. Find the mass M needed to balance the 150kg truck on the incline shown in the figure below. The angle of inclination θ is 45º. Assume all pulleys are frictionless and massless kg a) 80.0 mn ccw b) 69.3 mn ccw c) 40.0 mn ccw d) 34.6 mn cw e) 0 f) Calculate the resultant torque about point O for the two forces applied in the figure below. 28 mn cw 40. Calculate the net torque (magnitude and direction) on the beam shown in the figure below about a) an axis through O, perpendicular to the figure mn ccw b) an axis through C, perpendicular to the figure mn ccw Rotational Dynamics: In studying translational dynamics we made use of Newton's Second Law, which related the acceleration of a body and the forces applied to the body. An analogous relationship exists between angular acceleration and a quantity we call a torque. Qualitatively speaking, torque is the tendency of a force to cause a rotation of the body on which it acts. Mathematically speaking, torque is defined as the cross product of the moment arm and the applied force. The moment arm is the perpendicular distance between the force applied and the axis of rotation. The unit for torque is a meternewton. The symbol for torque is the lowercase Greek letter tau, τ. 44. A net force of 10.0 N is applied tangentially to the rim of a wheel having a 0.25 m radius. If the rotational inertia of the wheel is kg m 2, what is its angular acceleration? 5 rad/s A solid ball is rotated by applying a force of 4.7 N tangentially to it. The ball has a radius of 14 cm and a mass of 4.0 kg. What is the angular acceleration of the ball? 21 rad/s A fly wheel in the shape of a thin ring has a mass of 30.0 kg and a diameter of 0.96 m. A torque of 13 mn is applied tangentially to the wheel. How long will it take for the flywheel to attain an angular velocity of 10.0 rad/s? 5.3 sec
6 47. A cord is wrapped around the rim of a flywheel 0.5 m in radius, and a steady pull of 50.0 N is exerted on the cord. The wheel is mounted with frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel is 4.0 kgm 2. Compute the angular acceleration of the wheel rad/s A grindstone in the shape of a solid disk with a diameter of 1.0 m and a mass of 50.0 kg, is rotating at 900 rev/min. A tool is pressed against the rim with a normal force of N, and the grindstone comes to rest in 10.0 s. Find the coefficient of friction between the tool and the grindstone. Neglect friction in the bearings A bucket of water of mass 20.0 kg is suspended by a rope wrapped around a windlass in the form of a solid cylinder 0.20 m in diameter, also of mass 20.0 kg. The cylinder is pivoted on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 20.0 m to the water. Neglect the weight of the rope. a) What is the tension in the rope while the bucket is falling? 65.3N b) With what velocity does the bucket strike the water? 16.2 m/s c) What was the time of fall? 2.48 sec d) While the bucket is falling, what is the force exerted on the cylinder by the axle? 261 N 50. A 60.0kg grindstone is 1.0 m in diameter and has a moment of inertia of 3.75 kgm 2. A tool is pressed down on the rim with a normal force of 50.0 N. The coefficient of sliding friction between the tool and the stone is 0.6, and there is a constant friction torque of 5 mn between the axle of the stone and its bearings. a) How much force must be applied normally at the end of a crank handle 0.5 m long to bring the stone from rest to120 rev/min in 9.0 s? 50.5 N b) After attaining a speed of 120 rpm, what must the normal force at the end of the handle become to maintain a constant speed of 120 rpm? 40.0 N c) How long will it take the grindstone to come from 120 rpm to rest if it is acted on by the axle friction alone? 9.42 s 51. Dirk the Dragonslayer is exploring a castle. He is spotted by a dragon who chases him down a hallway. Dirk runs into a room and attempts to swing the heavy door shut before the dragon gets him. The door is initially perpendicular to the wall, so it must be turned through 90º to close. The door is 3.00 m tall and 1.00 m wide and weighs N. The friction at the hinges can be neglected. If Dirk applies a force of N at the edge of the door and perpendicular to it, how long will it take him to close the door? sec 52. A 5.0 kg block rests on a frictionless horizontal surface. A cord attached to the block passes over a pulley whose diameter is 0.2 m, to a hanging block also of mass 5.0 kg. The system is released from rest, and the blocks are observed to move 4.0 m in 2.0 seconds. a) What is the tension in each part of the cord? 10 N 39N b) What is the moment of inertia of the pulley? kgm Two blocks, one of mass 4.0 kg and the other of mass 2.0 kg are connected by a light rope that passes over a pulley as shown in the figure to the right. The pulley has radius 0.10 m and moment of inertia 0.20 kgm 2. Find the linear accelerations of Blocks A and B, the angular acceleration of wheel C, and the tension in each side of the cord a) if the surface of the wheel is frictionless; a A = a B = 3.27 m/s 2 ; a C = 0; T A = T B = 26.1 N b) if there is no slipping between the cord and the surface of the wheel. a A = a B = m/s 2 ; a C = 7.45 rad/s 2 ; T A = 36.2 N; T B = 21.1 N 54. A block of mass m = 5 kg slides down a surface inclined 37º to the horizontal, as shown in the figure to the right. The coefficient of sliding friction is A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has a mass of 20.0 kg, and outer radius of 0.2 m, and a moment of inertia with respect to the axis of 0.2 kgm 2. a) What is the acceleration of the block down the plane? 1.97 m/s 2 b) What is the tension in the string? 9.85 N 55. A flywheel 1.0 m in diameter is pivoted on a horizontal axis. A rope is wrapped around the outside of the flywheel, and a steady pull of 50.0 N is exerted on the rope. Ten meters of rope are unwound in 4.0 s. a) What is the angular acceleration of the flywheel? b) What is its final angular velocity? 2.5 rad/s 2 10 rad/s c) What is its final kinetic energy? 500 J d) What is its moment of inertia? 10 kgm 2
7 Heavy Pulleys and Hanging Masses: 1. A 4.0 kg bicycle wheel (Mass is concentrated at the rim.) of radius 0.20 m is held on a fixed support, while a 1.1 kg mass on a string wrapped around the wheel falls as shown. What is the linear acceleration of the dropping mass? 2.11 m/s 2 2. An Atwood machine is constructed using a massive 2.0 kg hoop of 22 cm radius as shown in the diagram. A 1.5 kg mass and a 1.0 kg mass arranged as shown are released from rest. Find the linear acceleration of the falling mass m/s 2 6. An Atwood machine consists of a disk of mass M, and radius R, and two masses ml and m 2 hanging from each side as shown in the figure. Find the linear acceleration of the system. 7. A 2disk Atwood machine with radii of 15 cm and 38 cm, has a moment of inertia of 4.0 kgm 2 is shown in the figure below. Masses of 3.0 kg and 2.0 kg are attached to strings wrapped around the disks as shown. When released from rest, what is the linear acceleration of each mass? a 2 = m/s 2 a 1 = m/s 2 3. A bicycle wheel of radius 0.70 m and mass 3.0 kg has a small light hub of radius 0.13 m as shown in the figure. The 2.0 kg mass which is attached to a string wrapped around the hub is released from rest. What is the linear acceleration of the dropping mass? m/s 2 9. A spool (solid cylinder) of radius 27 cm is mounted to spin about its axis. A string wrapped around it is pulled with a 5.4 N force, causing the object to spin up at 14 rad/sec 2. What is the moment of inertia of the object? kgm 2 4. An Atwood machine is constructed using two wheels (Mass concentrated at the rim.) as shown in the figure below. What is the linear acceleration of the hanging masses? 5. Find the linear acceleration of the system shown in the figure below. The mass of the pulley is concentrated at the rim. The coefficient of kinetic friction between the ramp and the 5.0 kg block is m/s 2
8 Angular Momentum and Angular Impulse: The angular momentum of a rigid body about a fixed axis is defined two ways: of the remainder of her body is constant and equal to 3.0 kgm rad/s if arms considered hollow cylinder L = Iω and For a single particle, the angular momentum relative to any point would be:...where m is the mass of the particle, r is the position vector from the point to the particle and v is the translational velocity. The product of the torque and the time interval during which it acts is called the angular impulse, J θ. The angular impulse acting on the body causes a change in the angular momentum of the body about the same axis. For a torque that varies with time, the angular impulse is defined as: Conservation of angular momentum states that when the net external torque on a system is zero, the angular momentum of the system remains constant. This principle of conservation of angular momentum ranks with the principles of conservation of linear momentum and conservation of energy as one of the most fundamental of physical laws. 19. Calculate the angular momentum of a uniform sphere of radius 0.20 m and mass 4.0 kg if it is rotating about an axis along a diameter at (a) 6.0 rad/s and (b) 5.0 rev/s. 2.0 kgm 2 /sec 20. A solid wooden door 1.0 m wide and 2.0 m high is hinged along one side and has a total mass of 50.0 kg. Initially open and at rest, the door is struck at its center with a hammer. During the blow and average force of N acts for 0.01 seconds. Find the angular velocity of the door after the impact. 21. A man of mass 70.0 kg is standing on the rim of a large disk that is rotating at 0.5 rev/s about an axis through its center. The disk has mass kg and radius 4.0 m. Calculate the total angular momentum of the manplusdisk system. 22. The outstretched arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center. When her arms are brought in and wrapped around her body to execute the spin, they can be considered a thinwalled hollow cylinder. If her original angular velocity is 6.28 rad/s, what is her final angular velocity? Her arms have a combined mass of 8.0 kg. When outstretched they span 1.8 m; when wrapped, they form a cylinder of radius 25 cm. (A disk and a cylinder rotating about an axis through the center have the same moment of inertia.) The moment of inertia
9 Equilibrium of Rigid Body: Recall that we said the first condition for equilibrium existed when the sum of the forces acting on the body was zero. Now we introduce the second condition for equilibrium which exists when the sum of the torques of all the forces acting on the body, with respect to any specified axis is zero. This means that the body is not accelerating and it is not rotating. If it were rotating then it would experience a centripetal acceleration. 21. A N weight is hung on the end of a horizontal pole 2.0 m long. What is the torque around the other end of the pole caused by this weight? Around the center of the pole? 400 mn 200 mn 22. Two men carry a 1500 N load by hanging it from a horizontal pole that rests on one shoulder of each man. If the men are 3.00 m apart and the load is 1.00 m from one of them, how much load does each man support? The weight of the pole is 500 N N 750 N 23. A man holds a m fishing pole horizontally with both hands, one at the end and the other m from the end. He has just caught a kg fish. The pole has a mass of kg and you can consider its weight to be concentrated m from the end near the man's hands. What is the force exerted by each hand? 93 N down 118 N up 24. A steel beam of uniform cross section weighs 2.5 x10 5 N. If it is 5.00 m long, what force is needed to lift one end of it? 1.2 x 10 5 N 25. A bar 4.0 m long weighs N. Its center of gravity is 1.5 m from one end. A weight of N is attached at the heavy end and a weight of N is attached at the light end. What are the magnitude, direction, and point of application of the force needed to achieve translational and rotational equilibrium of the bar? N up at 2.2 m from 300 N 26. A painter weighing 875 N stands on a plank 3.00 m long, which is supported at each end by a stepladder. The plank weighs 223 N. If the painter stands 1.00 m from one end of the plank, what force is exerted by each stepladder? 400 N 700 N 27. A brick layer weighing N stands 1.00 m from one end of a scaffold 3.00 m long. The scaffold weighs750 N. A pile of bricks weighing N is 1.50 m from the other end of the scaffold. What force must be exerted on each end of the scaffold in order to support it? 1070 N at end near bricklayer 800 N other end
10 Conceptual Questions: 1. Does a record player needle ride faster or slower over the groove at the beginning or the end of the record? If fidelity increases with translational speed, what part of the record produces the highest fidelity? 2. Suppose the first and last selections on a phonograph record are 3minutes cuts. Which, if either, of these cuts is wider on the record? (That is, which contains more grooves along a radial direction?) 3. Which moves faster on a merrygoround, a horse near the center or one near the outside. 4. If you use large diameter tires on your car, how will your speedometer reading differ? 5. Why are the front wheels located so far out in front on the racing vehicle? 6. Which will roll down a hill faster, a cylinder or a sphere of equal radii? A hollow cylinder or a solid cylinder of equal radii? Explain. 7. Why do buses and heavy trucks have large steering wheels? 8. Which is easier for turning stubborn screws, a screwdriver with a thick handle or one with a long handle? Explain. 9. Why is the middle seating most comfortable in a bus traveling on a bumpy road? 10. Explain why a long pole is more beneficial to a tightrope walker if it droops. 11. Why do you bend forward when carrying a heavy load on your back? 12. Why is it easier to carry the same amount of water in two buckets, one in each hand, then in a single bucket? 13. Using the ideas of torque and center of gravity, explain why a ball rolls down a hill. 14. Why is it dangerous to roll open the top drawers of a fully loaded file cabinet that is not secured to the floor? 15. Why is less effort required in doing situps when your arms are extended in front of you? Why is it more difficult when your arms are placed in back of your head? 16. For a rotating wheel, how do the directions of the linear velocity vector and the angular velocity vector compare at the same instant of time? Answers to conceptual questions: 1. The phonograph needle rides faster at the beginning of the record. Since fidelity is enhanced with translational speed, then fidelity would be best at the beginning of a record. 2. Both three minute selections would have the same width because they would make the same number of revolutions during a three minute time period. 3. The horse on the outer rail has a greater translational (tangential) speed, while both have the same rotational speed. 4. The circumference of a large diameter tire is greater, meaning it will move a greater distance per revolution, which results in a greater speed than that shown on the speedometer. 5. The long distance to the front wheels increases the rotational inertia of the vehicle without appreciably adding to its weight. As the back wheels are driven clockwise, the rest of the car tends to rotate counterclockwise. This would lift the front wheels off the ground. 6. A sphere will roll faster because it has less rotational inertia than a cylinder. A solid cylinder will roll faster than a hollow cylinder for the same reason. 7. The large radius of a large steering wheel allows the driver to exert more torque for a given force. 8. More torque can be exerted by the screw driver having a thick handle. 9. A rocking bus rocks about its center of gravity which is around the center of the bus. It works something like a seesaw  the farther from the center, the more you go up and down. 10. The long drooping pole lowers the center of gravity of the pole and the tightrope walker. The pole contributes to his rotational inertia. 11. You bend forward to shift the center of gravity of you and the back pack. If you did not shift the center of gravity over the support, you would topple over. 12. There is no need to adjust your center of gravity if the water is distributed between the two buckets. 13. When a ball is on an incline its center of gravity is not above the point of support. The weight acts some distance from the point of support and produces a torque about the point of support. 14. The center of gravity could be adjusted so that it is no longer above the support. 15. When your arms are extended in front of you while doing situps, not only are they not lifted as far, they are closer to the axis of rotation and give you less rotational inertia. When behind your head they are lifted farther and their farther distance from the axis of rotation increases your rotational inertia.
Textbook Reference: Wilson, Buffa, Lou: Chapter 8 Glencoe Physics: Chapter 8
AP Physics Rotational Motion Introduction: Which moves with greater speed on a merrygoround  a horse near the center or one near the outside? Your answer probably depends on whether you are considering
More informationName: Date: Period: AP Physics C Rotational Motion HO19
1.) A wheel turns with constant acceleration 0.450 rad/s 2. (99) Rotational Motion H19 How much time does it take to reach an angular velocity of 8.00 rad/s, starting from rest? Through how many revolutions
More informationRotation. PHYS 101 Previous Exam Problems CHAPTER
PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that
More informationWebreview Torque and Rotation Practice Test
Please do not write on test. ID A Webreview  8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30mradius automobile
More informationSlide 1 / 133. Slide 2 / 133. Slide 3 / How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m?
1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 1 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 2 / 133 3 A ball rotates
More informationSlide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133
Slide 1 / 133 1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 2 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 3 / 133
More informationBig Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular
Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationRotational Mechanics Part III Dynamics. Pre AP Physics
Rotational Mechanics Part III Dynamics Pre AP Physics We have so far discussed rotational kinematics the description of rotational motion in terms of angle, angular velocity and angular acceleration and
More informationRolling, Torque, and Angular Momentum
AP Physics C Rolling, Torque, and Angular Momentum Introduction: Rolling: In the last unit we studied the rotation of a rigid body about a fixed axis. We will now extend our study to include cases where
More informationAP Physics 1: Rotational Motion & Dynamics: Problem Set
AP Physics 1: Rotational Motion & Dynamics: Problem Set I. Axis of Rotation and Angular Properties 1. How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 2. How many degrees are
More informationChapter 8  Rotational Dynamics and Equilibrium REVIEW
Pagpalain ka! (Good luck, in Filipino) Date Chapter 8  Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body
More informationTest 7 wersja angielska
Test 7 wersja angielska 7.1A One revolution is the same as: A) 1 rad B) 57 rad C) π/2 rad D) π rad E) 2π rad 7.2A. If a wheel turns with constant angular speed then: A) each point on its rim moves with
More informationEndofChapter Exercises
EndofChapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. Figure 11.21 shows four different cases involving a
More informationUnit 8 Notetaking Guide Torque and Rotational Motion
Unit 8 Notetaking Guide Torque and Rotational Motion Rotational Motion Until now, we have been concerned mainly with translational motion. We discussed the kinematics and dynamics of translational motion
More informationName Date Period PROBLEM SET: ROTATIONAL DYNAMICS
Accelerated Physics Rotational Dynamics Problem Set Page 1 of 5 Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Directions: Show all work on a separate piece of paper. Box your final answer. Don t forget
More informationChapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balancethetorques lab as an inquiry introduction
Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balancethetorques lab as an inquiry introduction 1. The distance between a turning axis and the
More informationTutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning?
1. rpm is about rad/s. 7. ROTATIONAL MOTION 2. A wheel rotates with constant angular acceleration of π rad/s 2. During the time interval from t 1 to t 2, its angular displacement is π rad. At time t 2
More informationChapter 8 Lecture Notes
Chapter 8 Lecture Notes Physics 2414  Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ
More informationAdvanced Higher Physics. Rotational motion
Wallace Hall Academy Physics Department Advanced Higher Physics Rotational motion Problems AH Physics: Rotational Motion 1 2013 Data Common Physical Quantities QUANTITY SYMBOL VALUE Gravitational acceleration
More informationThe student will be able to: 1 Determine the torque of an applied force and solve related problems.
Honors Physics Assignment Rotational Mechanics Reading Chapters 10 and 11 Objectives/HW The student will be able to: HW: 1 Determine the torque of an applied force and solve related problems. (t = rx r
More informationRolling, Torque & Angular Momentum
PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the
More informationWe define angular displacement, θ, and angular velocity, ω. What's a radian?
We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise
More information31 ROTATIONAL KINEMATICS
31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have
More informationName: Date: 5. A 5.0kg ball and a 10.0kg ball approach each other with equal speeds of 20 m/s. If
Name: Date: 1. For this question, assume that all velocities are horizontal and that there is no friction. Two skaters A and B are on an ice surface. A and B have the same mass M = 90.5 kg. A throws a
More informationPhysics. Chapter 8 Rotational Motion
Physics Chapter 8 Rotational Motion Circular Motion Tangential Speed The linear speed of something moving along a circular path. Symbol is the usual v and units are m/s Rotational Speed Number of revolutions
More informationRotational Motion and Torque
Rotational Motion and Torque Introduction to Angular Quantities Sections 8 to 82 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is
More informationSuggested Problems. Chapter 1
Suggested Problems Ch1: 49, 51, 86, 89, 93, 95, 96, 102. Ch2: 9, 18, 20, 44, 51, 74, 75, 93. Ch3: 4, 14, 46, 54, 56, 75, 91, 80, 82, 83. Ch4: 15, 59, 60, 62. Ch5: 14, 52, 54, 65, 67, 83, 87, 88, 91, 93,
More informationChapter 910 Test Review
Chapter 910 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular
More information= o + t = ot + ½ t 2 = o + 2
Chapters 89 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
More information1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merrygoround rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,
More informationCHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque
7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity
More informationMoment of Inertia Race
Review Two points, A and B, are on a disk that rotates with a uniform speed about an axis. Point A is closer to the axis than point B. Which of the following is NOT true? 1. Point B has the greater tangential
More informationAP Physics 1 Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law F = Ma cm. Usually the location of the center
More informationUse the following to answer question 1:
Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to
More informationReview questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.
Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the
More informationChapter 10. Rotation
Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGrawPHY 45 Chap_10HaRotationRevised
More information3. A bicycle tire of radius 0.33 m and a mass 1.5 kg is rotating at 98.7 rad/s. What torque is necessary to stop the tire in 2.0 s?
Practice 8A Torque 1. Find the torque produced by a 3.0 N force applied at an angle of 60.0 to a door 0.25 m from the hinge. What is the maximum torque this force could exert? 2. If the torque required
More informationChapter 8, Rotational Equilibrium and Rotational Dynamics. 3. If a net torque is applied to an object, that object will experience:
CHAPTER 8 3. If a net torque is applied to an object, that object will experience: a. a constant angular speed b. an angular acceleration c. a constant moment of inertia d. an increasing moment of inertia
More informationLecture Presentation Chapter 7 Rotational Motion
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
More informationThe student will be able to: the torque of an applied force and solve related problems.
Honors Physics Assignment Rotational Mechanics Reading Chapters 10 and 11 Objectives/HW: Assignment #1 M: Assignment #2 M: Assignment #3 M: Assignment #4 M: 1 2 3 #15 #610 #14, 15, 17, 18, 2023 #24,
More informationCircular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics
Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #2 November 16, 2000 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION
More informationPhys 106 Practice Problems Common Quiz 1 Spring 2003
Phys 106 Practice Problems Common Quiz 1 Spring 2003 1. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed
More informationDynamics of Rotational Motion: Rotational Inertia
Dynamics of Rotational Motion: Rotational Inertia Bởi: OpenStaxCollege If you have ever spun a bike wheel or pushed a merrygoround, you know that force is needed to change angular velocity as seen in
More informationRotational Dynamics, Moment of Inertia and Angular Momentum
Rotational Dynamics, Moment of Inertia and Angular Momentum Now that we have examined rotational kinematics and torque we will look at applying the concepts of angular motion to Newton s first and second
More informationChapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium
More information6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.
1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular
More informationExercise Torque Magnitude Ranking Task. Part A
Exercise 10.2 Calculate the net torque about point O for the two forces applied as in the figure. The rod and both forces are in the plane of the page. Take positive torques to be counterclockwise. τ 28.0
More informationPHYSICS 149: Lecture 21
PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30
More informationIt will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV
AP Physics 1 Lesson 16 Homework Newton s First and Second Law of Rotational Motion Outcomes Define rotational inertia, torque, and center of gravity. State and explain Newton s first Law of Motion as it
More informationChapter 10 Practice Test
Chapter 10 Practice Test 1. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of 0.40 rad/s 2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What
More informationAPC PHYSICS CHAPTER 11 Mr. Holl Rotation
APC PHYSICS CHAPTER 11 Mr. Holl Rotation Student Notes 111 Translation and Rotation All of the motion we have studied to this point was linear or translational. Rotational motion is the study of spinning
More informationAP practice ch 78 Multiple Choice
AP practice ch 78 Multiple Choice 1. A spool of thread has an average radius of 1.00 cm. If the spool contains 62.8 m of thread, how many turns of thread are on the spool? "Average radius" allows us to
More informationPhysics for Scientist and Engineers third edition Rotational Motion About a Fixed Axis Problems
A particular bird s eye can just distinguish objects that subtend an angle no smaller than about 3 E 4 rad, A) How many degrees is this B) How small an object can the bird just distinguish when flying
More informationPhysics 130: Questions to study for midterm #1 from Chapter 8
Physics 130: Questions to study for midterm #1 from Chapter 8 1. If the beaters on a mixer make 800 revolutions in 5 minutes, what is the average rotational speed of the beaters? a. 2.67 rev/min b. 16.8
More informationChapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.
Chapter 9 [ Edit ] Chapter 9 Overview Summary View Diagnostics View Print View with Answers Due: 11:59pm on Sunday, October 30, 2016 To understand how points are awarded, read the Grading Policy for this
More informationLecture 3. Rotational motion and Oscillation 06 September 2018
Lecture 3. Rotational motion and Oscillation 06 September 2018 Wannapong Triampo, Ph.D. Angular Position, Velocity and Acceleration: Life Science applications Recall last t ime. Rigid Body  An object
More informationRotation Quiz II, review part A
Rotation Quiz II, review part A 1. A solid disk with a radius R rotates at a constant rate ω. Which of the following points has the greater angular velocity? A. A B. B C. C D. D E. All points have the
More informationRotation. Rotational Variables
Rotation Rigid Bodies Rotation variables Constant angular acceleration Rotational KE Rotational Inertia Rotational Variables Rotation of a rigid body About a fixed rotation axis. Rigid Body an object that
More informationAngular Speed and Angular Acceleration Relations between Angular and Linear Quantities
Angular Speed and Angular Acceleration Relations between Angular and Linear Quantities 1. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles. (a) Determine the
More informationPhysics 53 Exam 3 November 3, 2010 Dr. Alward
1. When the speed of a reardrive car (a car that's driven forward by the rear wheels alone) is increasing on a horizontal road the direction of the frictional force on the tires is: A) forward for all
More informationDescription: Using conservation of energy, find the final velocity of a "yo yo" as it unwinds under the influence of gravity.
Chapter 10 [ Edit ] Overview Summary View Diagnostics View Print View with Answers Chapter 10 Due: 11:59pm on Sunday, November 6, 2016 To understand how points are awarded, read the Grading Policy for
More informationExam 3 PREP Chapters 6, 7, 8
PHY241  General Physics I Dr. Carlson, Fall 2013 Prep Exam 3 PREP Chapters 6, 7, 8 Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Astronauts in orbiting satellites
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 1
Physics 12 Unit 5 Circular Motion and Gravitation Part 1 1. Nonlinear motions According to the Newton s first law, an object remains its tendency of motion as long as there is no external force acting
More informationChapter 8 Rotational Motion
Chapter 8 Rotational Motion Chapter 8 Rotational Motion In this chapter you will: Learn how to describe and measure rotational motion. Learn how torque changes rotational velocity. Explore factors that
More informationAP Physics QUIZ Chapters 10
Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5kilogram sphere is connected to a 10kilogram sphere by a rigid rod of negligible
More informationAP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems
AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is
More informationAngular Motion Unit Exam Practice
Angular Motion Unit Exam Practice Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. If you whirl a tin can on the end of a string and the string suddenly
More informationAP Physics 1 Rotational Motion Practice Test
AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is
More informationPhysics 201 Midterm Exam 3
Physics 201 Midterm Exam 3 Information and Instructions Student ID Number: Section Number: TA Name: Please fill in all the information above. Please write and bubble your Name and Student Id number on
More informationCircular Motion Tangential Speed. Conceptual Physics 11 th Edition. Circular Motion Rotational Speed. Circular Motion
Conceptual Physics 11 th Edition Circular Motion Tangential Speed The distance traveled by a point on the rotating object divided by the time taken to travel that distance is called its tangential speed
More informationCentripetal acceleration ac = to2r Kinetic energy of rotation KE, = \lto2. Moment of inertia. / = mr2 Newton's second law for rotational motion t = la
The Language of Physics Angular displacement The angle that a body rotates through while in rotational motion (p. 241). Angular velocity The change in the angular displacement of a rotating body about
More informationTorque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.
Warm up A remotecontrolled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics
More informationVersion A (01) Question. Points
Question Version A (01) Version B (02) 1 a a 3 2 a a 3 3 b a 3 4 a a 3 5 b b 3 6 b b 3 7 b b 3 8 a b 3 9 a a 3 10 b b 3 11 b b 8 12 e e 8 13 a a 4 14 c c 8 15 c c 8 16 a a 4 17 d d 8 18 d d 8 19 a a 4
More informationChapter 9: Rotational Dynamics Tuesday, September 17, 2013
Chapter 9: Rotational Dynamics Tuesday, September 17, 2013 10:00 PM The fundamental idea of Newtonian dynamics is that "things happen for a reason;" to be more specific, there is no need to explain rest
More informationEndofChapter Exercises
EndofChapter Exercises For all these exercises, assume that all strings are massless and all pulleys are both massless and frictionless. We will improve our model and learn how to account for the mass
More informationPS 11 GeneralPhysics I for the Life Sciences
PS 11 GeneralPhysics I for the Life Sciences ROTATIONAL MOTION D R. B E N J A M I N C H A N A S S O C I A T E P R O F E S S O R P H Y S I C S D E P A R T M E N T F E B R U A R Y 0 1 4 Questions and Problems
More informationPHYSICS 221 SPRING 2014
PHYSICS 221 SPRING 2014 EXAM 2: April 3, 2014 8:1510:15pm Name (printed): Recitation Instructor: Section # INSTRUCTIONS: This exam contains 25 multiplechoice questions plus 2 extra credit questions,
More informationTopic 1: Newtonian Mechanics Energy & Momentum
Work (W) the amount of energy transferred by a force acting through a distance. Scalar but can be positive or negative ΔE = W = F! d = Fdcosθ Units N m or Joules (J) Work, Energy & Power Power (P) the
More informationAngular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion
Angular velocity and angular acceleration CHAPTER 9 ROTATION! r i ds i dθ θ i Angular velocity and angular acceleration! equations of rotational motion Torque and Moment of Inertia! Newton s nd Law for
More informationΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω
Thur Oct 22 Assign 9 Friday Today: Torques Angular Momentum x θ v ω a α F τ m I Roll without slipping: x = r Δθ v LINEAR = r ω a LINEAR = r α ΣF = ma Στ = Iα ½mv 2 ½Iω 2 I POINT = MR 2 I HOOP = MR 2 I
More informationFall 2007 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton
Fall 007 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton 3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.
More informationChapter 8: Rotational Motion
Lecture Outline Chapter 8: Rotational Motion This lecture will help you understand: Circular Motion Rotational Inertia Torque Center of Mass and Center of Gravity Centripetal Force Centrifugal Force Rotating
More informationQuantitative Skills in AP Physics 1
This chapter focuses on some of the quantitative skills that are important in your AP Physics 1 course. These are not all of the skills that you will learn, practice, and apply during the year, but these
More information第 1 頁, 共 7 頁 Chap10 1. Test Bank, Question 3 One revolution per minute is about: 0.0524 rad/s 0.105 rad/s 0.95 rad/s 1.57 rad/s 6.28 rad/s 2. *Chapter 10, Problem 8 The angular acceleration of a wheel
More informationRotational Motion What is the difference between translational and rotational motion? Translational motion.
Rotational Motion 1 1. What is the difference between translational and rotational motion? Translational motion Rotational motion 2. What is a rigid object? 3. What is rotational motion? 4. Identify and
More informationPHYS 1303 Final Exam Example Questions
PHYS 1303 Final Exam Example Questions 1.Which quantity can be converted from the English system to the metric system by the conversion factor 5280 mi f 12 f in 2.54 cm 1 in 1 m 100 cm 1 3600 h? s a. feet
More informationRotational Kinematics and Dynamics. UCVTS AIT Physics
Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,
More informationAP Physics Multiple Choice Practice Torque
AP Physics Multiple Choice Practice Torque 1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44
More informationPhysics 211 Sample Questions for Exam IV Spring 2013
Each Exam usually consists of 10 Multiple choice questions which are conceptual in nature. They are often based upon the assigned thought questions from the homework. There are also 4 problems in each
More informationClass XI Chapter 7 System of Particles and Rotational Motion Physics
Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Common Quiz Mistakes / Practice for Final Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A ball is thrown directly upward and experiences
More informationConcept Question: Normal Force
Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical
More informationDynamics of Rotational Motion: Rotational Inertia
Connexions module: m42179 1 Dynamics of Rotational Motion: Rotational Inertia OpenStax College This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License
More informationPhysics 23 Exam 3 April 2, 2009
1. A string is tied to a doorknob 0.79 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the torque on the door? A) 3.3 N m B) 2.2 N m C)
More informationRotational Kinetic Energy
Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body
More informationVersion 001 Rotational Motion ramadoss (171) 1
Version 001 Rotational Motion ramadoss (171) 1 This printout should have 48 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. Please do the
More information