Rotational Motion What is the difference between translational and rotational motion? Translational motion.

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1 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 define the parts of a rotating object # Term What is it? Unit

2 Rotational motion 2 5. What is the relationship between radius, arc length and angle? 6. Define a radian 7. What is the purpose of a radian? Linear motion Sphere Radius Circumference speed Rotational motion Sphere Radians Angular speed 1 2 3

3 Rotational motion 3 problem : How many radians does the minute hand on a clock sweep through in 3.5 hours? How many degrees? A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle θ of 1.4 x 10-5 rad. What diameter spot will it make on the Moon? 8. How else can angular motion be described? 9. Complete the following chart Radians Degrees 3π π 10. Define angular displacement Term Formula Scalar/Vector SI Unit Show angular displacement

4 Rotational motion Define average angular velocity Term Formula Scalar/Vector SI Unit The rotor on a helicopter turns at an angular velocity of 320 rpm. What is its angular speed? 12. How is the direction of angular velocity determined? 13. What is the relationship between angular velocity and tangential velocity? 14. Define average angular acceleration Term Formula Scalar/Vector SI Unit 15. What is the relationship between angular acceleration and tangential acceleration? 16. What acceleration can a rotating object have?

5 Rotational motion Show the linear constant acceleration equations and their angular counterparts. What is the number one rule for these problems? What is missing Linear Equation Angular Equation problem A bicycle wheel rotates with a constant angular acceleration of 3.5 rad/s2. If the initial angular speed of the wheel is 2.0 rad/s at t = 0 s, Through what angle does the wheel rotate in 2.0 s? problem A phonograph turntable reaches its speed of 33 rpm after making 1.7 revolutions. What was its angular acceleration? 18. How can centripetal acceleration be found?

6 Rotational motion 6 A bicycle slows down uniformly from v = 8.40 m/s to rest over a distance of 115 m. Each wheel and tire has an overall diameter of 68.0 cm. Determine : a. the angular velocity of the wheels at the initial instant (t=0) b. the total number of revolutions each wheel rotates before coming to rest c. the angular acceleration of the wheel d. the time it took to stop The platter of the hard disk of a computer rotates at 5400 rpm. What is the angular velocity of the disk? If the reading head of the drive is located 3.0 cm from the rotation axis, what is the speed of the disk below it. What is the linear acceleration of this point? If a single bit requires 5 µm of length along the motion direction, how may bits per second can the writing head write when it is 3.0 cm from the axis?

7 Rotational motion Define Torque Variable Formula Vector/scalar SI 20. What is a cross product? 21. What is the lever arm (moment arm)? How is it defined? d F Show the diagram of the wrench drawn by your teacher and identify how the torque would be calculated. F= 100 θ= 30 0 d=.15 m 22. How does the force and the lever arm effect torque? 23. How can the direction of torque be determined?

8 Rotational motion 8 Find the torque produced by a 300 N force applied at an angle of 60 0 to the door shown in the figure N 2.0m What are the two conditions for Equilibrium? Condition 1 Condition 2 Two children are playing on a teeter toter made up of a board of mass 2.0 kg sitting on a log. The child on the left has a mass of 30. kg and sits 1.5 m from the log. The child on the right has a mass of 20. kg. How far out on the board must child B sit to balance the teeter toter? What force must the log supply?

9 Rotational motion 9 A 50.0 N weight is held in a person s hand with the forearm horizontal, as shown. The biceps muscle is attached.0300 m from the elbow, and the weight is.350 m from the elbow. Find the upward force exerted on the forearm (the ulna) by the biceps and the downward force on the forearm (the humerus) acting at the elbow. Neglect the weight of the forearm. A uniform, horizontal 300 N beam, 5.00 m long, is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of with the horizontal. If a 600. N person stands 1.50 m from the wall, find the tension in the cable and the force exerted on the beam by the wall. A uniform 10. m long, 50. N ladder rests against a smooth vertical wall as shown. If the ladder is just on the verge of slipping when the angle it makes with the ground is 50. 0, find the coefficient of static friction between the ladder and the ground.

10 Rotational motion What is the relationship between Torque and angular acceleration? 26. What is the moment of inertia and how does it affect rotation? Variable Formula Vector/scalar SI Which has a greater I, a thin hoop or a solid sphere? Why? Two small weights of mass 5.0 kg and 7.0kg, are mounted 4.0 m apart on a light rod(whose mass can be ignored). Calculate the moment of inertia of the system a) when rotated about an axis halfway between the weights b) When rotated about an axis.50 m to the left of the 5.0 kg mass A baseball player loosening up his arm before a game tosses a.15 kg baseball using only the rotation of his forearm to accelerate the ball. The ball starts at rest and is released with a speed of 30.0 m/s in.300 s

11 Rotational motion Define Rotational Kinetic Energy Variable Formula Vector/scalar SI Several objects roll without slipping down an incline of vertical height H, all starting from rest at the same moment. The objects are a thin hoop, a spherical marble, a solid cylinder, and an empty soup can. In addition, a greased box slides down without friction. In what order do they reach the bottom of the incline? 28. Define Angular Momentum Variable Formula Vector/scalar SI 28. Give some examples of the conservation of angular motion Ice Skater Rotation of a Star Rotating stool Diver

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