Chapter 8: Newton s Laws Applied to Circular Motion
|
|
- Christiana Dorsey
- 6 years ago
- Views:
Transcription
1 Chapter 8: Newton s Laws Applied to Circular Motion
2 Circular Motion
3 Milky Way Galaxy Orbital Speed of Solar System: 220 km/s Orbital Period: 225 Million Years
4 Mercury: 48 km/s Venus: 35 km/s Earth: 30 km/s Mars: 24 km/s Jupiter: 13 km/s Neptune: 5 km/s
5 Differential Solar Rotation Entangled Magentic Field Lines makes Sun Spots Equatorial Rotational Period: 27.5 days
6 464m/s
7 Precession causes the position of the North Pole to change over a period of 26,000 years.
8 Orbital Speed of Earth: ~ 30 km/s
9 Although the Moon is always lit from the Sun, we see different amounts of the lit portion from Earth depending on where the Moon is located in its month-long orbit. Orbital Speed of Moon: ~ 1 km/s
10 155mph~70m/s
11 RADAR: RAdio Detecting And Ranging 200mph~90m/s
12 Electrons in Bohr Orbit: 2 million m/s (Speed of Light: 200 million m/s)
13 Maximal Kerr Black Hole Rotational Speed = Speed of Light
14 Horizontal Circle: Constant Speed & Acceleration Vertical Circle: Changing Speed & Acceleration
15 Important: Inside vs Outside the Rotating Frame
16 Important: Inside vs Outside the Rotating Frame
17 Translational vs Rotational / / m x v dx dt a dv dt = = / / I d dt d dt θ ω θ α ω = = 2 / c t s r v r a v r a r θ ω α = = = = Connection
18 Translational and Rotational Kinematics For CONSTANT Accelerations ONLY
19 Angular Velocity in Uniform Circular Motion When angular velocity ω is constant, this is uniform circular motion. In this case, as the particle goes around a circle one time, its angular displacement is θ = 2π during one period t = T. ω: angular velocity (rad/s) 2013 Pearson Education, Inc. Slide 4-87
20 Angular Position: Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle, the greater the radius, the greater the arc length. = θ s r θ = rotation angle s = arc length r = radius
21 How many radians in 360 0? Ans: = 2 π radians Consider a circle with radius r. θ = s/r θ = 2 πr /r θ = 2 π r How many degrees in 1 radian? s =? s = C = 2πr 2 π rad = rad = /2 π =
22 θ r = 4 m s A box is fastened to a string that is wrapped around a pulley. The pulley turns through an angle of What is the distance, d, that the box moves? d 43 = 43 x1 = 43 x 2 =.75rad π 360 First: How many radians is 43 0?
23 θ r = 4 m s A box is fastened to a string that is wrapped around a pulley. The pulley turns through an angle of.75 rad. What is the distance, d, that the box moves? d s = r θ d = r θ d = 4m (0.75 rad) d = 3 m rad d = 3 m 43 0 =.75rad Radian is dimensionless and is dropped!
24 Angular Velocity ω: angular velocity (rad/s) θ ω = d dt ( / ) = ds r dt 1 = ds r dt = v r t
25 Angular & Tangential Velocity ω: angular velocity (rad/s) v: tangential velocity (m/s) θ d ω = = dt v r v = ωr ω is the same for every point & v varies with r.
26 Problem v = ωr Calculate the angular velocity of a m radius car tire when the car travels at a constant speed of 25.0 m/s. ω = v r = = 25 m/ s.5m 50 rad / s Insert rad for angular speed. Keep it to define units.
27 Tangential and Angular Acceleration changes speed a t dv = dt ( ω ) = d r dt v = ωr = d r dt ω ω α = d dt at = αr
28 Angular Tangential Bike A bike wheel with a radius of 0.25 m undergoes a constant angular acceleration of 2.50 rad/s 2. The initial angular speed of the wheel is 5.00 rad/s. After 4.00 s a) What angle has the wheel turned through? b) What is the final angular speed? c) What is the final tangential speed of the bike? d) How far did the bike travel? θ = ω0t+ αt = 5 rad / s4s rad / s (4 s) = 40rad ω = ω + αt = 5 rad / s rad / s 4s = 15 rad / s f 0 v = ωr = 15 rad / s.25m = 3.75 m / s d = s = θ r = 40 rad.25m = 10m ω Givens: 0 = 5 rad / s α = 2.5 rad / s t = 4s 2
29 Centripetal Acceleration v Centripetal Acceleration Only changes Direction!!! = ωr s = rθ ds d( rθ ) v = = dt dt dt = Combining: dr ( θ ) v a dv vdθ v = = = dt ( rdθ / v) r Pearson Education, Inc.
30 Centripetal and Tangential Accelerations at = αr a c = v r 2 = ( ωr) r 2 ac 2 = ω r (r constant)
31 Total Acceleration 2 2 r t a = a + a a= arˆ + aθθˆ r a = a = ω 2 r = v 2 / r r c a = a = αr = dv / dt θ t
32 Nonuniform Circular Motion a t = d dt v a r = a = C v r 2 a = a + a 2 2 r t
33 Circular Motion Total Acceleration The tangential acceleration causes the change in the speed of the particle a t = d v dt The radial acceleration comes from a change in the direction of the velocity vector a r = a = C v r 2 Total Acceleration: a = a + a 2 2 r t
34 Total Acceleration & Force a t = d dt v 2 a a = a + a r 2 2 r t = a = C v r 2 2 r F = F + F θ
35 Total Acceleration a c The total acceleration of a particle moving clockwise in a circle of radius 2.50 m at a certain of time is 15.0m/s 2. At this instant, find (a) the radial acceleration, (b) the speed of the particle, and (c) its tangential acceleration. v r ac 2 ( )( ) o 2 2 = acos30.0 = 15.0 m s cos30 = 13.0 m s = v ra ( ) c = t + r a a a = = 2.50 m 13.0 m s = 32.5 m s v = 32.5 m s = 5.70 m s r 15.0 m s 13.0m s 7.50 m s ( ) ( ) a = a a = = t
36 Centrifugal Force & Acceleration Center FLEEing Suppose there is a lady bug in the can. There is a centripetal force acting on the bug, transmitted to her feet by the can. Her feet push back on the can producing a centrifugal fictitious force, that acts like artificial gravity.
37 The Earth rotates once per day around its axis as shown. Assuming the Earth is a sphere, is the angular speed at Santa Rosa greater or less than the speed at the equator?
38 The Earth rotates once per day around its axis as shown. Assuming the Earth is a sphere, is the tangential speed at Santa Rosa greater or less than the speed at the equator? 366 m/s 464 m/s
39 Is the centripetal acceleration greater at the Equator or at Santa Rosa? a c v r m/ s = m/ s
40 The Earth rotates once per day around its axis. Assuming the Earth is a sphere with radius 6.38 x 10 6 m, find the tangential speed of a person at the equator and at 38 degrees latitude (Santa Rosa!) and their centripetal accelerations. At the equator, r = 6.38 x 10 6 m: 6 2πr 2 π(6.38x10 m) v= = = t 86, 400s a c ( 464 m/ s) 2 2 v = = = 6 r 6.38x10 m 464 m/ s.034 m/ s At Santa Rosa, r = 6.38 x 10 6 m cos38: 2 a c a c 6 2πr 2 π(6.38x10 m)cos38 v= = = t 86, 400s a c ( 366 m/ s) m/ s 2 v = = =.027 m/ s 6 r cos x10 m cos 38 2
41 What is the total acceleration acting on a person in Santa Rosa? The vector sum. a c g
42 Is your apparent weight as measured on a spring scale more at the Equator or at Santa Rosa? a c g
43 Since you are standing on the Earth (and not in the can) the centrifugal force tends to throw you off the Earth. You weigh less where the centripetal force is greatest because that is also where the centrifugal force is greatest the force that tends to throw you out of a rotating reference frame.
44 Centrifugal Force & Acceleration Center FLEEing F actual = Centripetal Force F fictitious = Centrifugal Force
45 Centrifugal Force & Acceleration Center FLEEing Suppose there is a lady bug in the can. There is a centripetal force acting on the bug, transmitted to her feet by the can. Her feet push back on the can producing a centrifugal fictitious force, that acts like artificial gravity.
46 Centripetal & Centrifugal Force Depends on Your Reference Frame Center-seeking Outside Observer (non-rotating frame) sees Centripetal Force pulling can in a circle. Center-fleeing Inside Observer (rotating reference frame) feels Centrifugal Force pushing them against the can.
47 Centrifugal Force is Fictitious? The centrifugal force is a real effect. Objects in a rotating frame feel a centrifugal force acting on them, trying to push them out. This is due to your inertia the fact that your mass does not want to go in a circle. The centrifugal force is called fictitious because it isn t due to any real force it is only due to the fact that you are rotating. The centripetal force is real because it is due to something acting on you like a string or a car.
48 In Physics, we use ONLY CentriPETAL acceleration NOT CentriFUGAL acceleration!
49 Coriolis Force This is an apparent force caused by changing the radial position of an object in a rotating coordinate system The result of the rotation is the curved path of the ball
50 Coriolis Force This is an apparent force caused by changing the radial position of an object in a rotating coordinate system The result of the rotation is the curved path of the ball
51 Coriolis Effect
52
53 Artificial Gravity How fast would the space station segments A and B have to rotate in order to produce an artificial gravity of 1 g? v = 56 m / s ~ 115mph A v = 104 m / s ~ 210mph B Can the two segments be connected?
54 Space Station Rotation A space station of diameter 80 m is turning about its axis at a constant rate. If the acceleration of the outer rim of the station is 2.5 m/s 2, what is the period of revolution of the space station? a. 22 s b. 19 s c. 25 s d. 28 s e. 40 s
55 Horizontal Circle: Constant Speed & Acceleration Vertical Circle: Changing Speed & Acceleration
56 Important: Inside vs Outside the Rotating Frame
57 Motion in a Horizontal Circle The speed at which the object moves depends on the mass of the object and the tension in the cord. It is constant! The centripetal force is supplied by the tension. Looking down: c F = T = ma = c mv r 2 v = Tr m
58 Motion in a Horizontal Circle
59 Horizontal Circle: Conical Pendulum y F = T cosθ = mg c F = T sinθ = ma = c mv r 2 Combining : r = Lsinθ v = Lg sinθ tanθ
60 Horizontal (Flat) Curve The force of static friction supplies the centripetal force Fc = f = The maximum speed at which the car can negotiate the curve is mv r 2 v µ gr Note, this does not depend on the mass of the car = y F = N mg =0 f = µ mg
61 Horizontal (Flat) Curve 3. A highway curve has a radius of 0.14 km and is unbanked. A car weighing 12 kn goes around the curve at a speed of 24 m/s without slipping. What is the magnitude of the horizontal force of the road on the car? What is μ? Draw FBD. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn
62 Banked Curve These are designed with friction equaling zero - there is a component of the normal force that supplies the centripetal force that keeps the car moving in a circle. Fr y 2 mv = nsinθ = r F = n cosθ mg = 0 Dividing: tanθ = 2 v rg
63 Banked Curve 4. A race car travels 40 m/s around a banked circular (radius = 0.20 km) track. What is the magnitude of the resultant force on the 80-kg driver of this car? a kn b kn c kn d kn e kn
64 Hints for HW Problem Determine the range of speeds a car can have without slipping up or down the road when it is banked AND has friciton. If the car is about to slip down the incline, f is directed up the incline. This would happen at a minimum speed. When the car is about to slip up the incline, f is directed down the incline. This would happen at a maximum speed.
65 Vertical Circle with Non-Uniform Speed Where is the speed Max? Min? Where is the Tension Max? Min?
66 Vertical Circle with Non-Uniform Speed The tension at the bottom is a maximum The tension at the top is a minimum Look at radial and tangential: t F = mg sinθ = ma t at = g sinθ r F = T mg cosθ = mv R 2 2 v T = m + g R cosθ
67 Vertical Circle: Mass on a String A 0.40-kg mass attached to the end of a string swings in a vertical circle having a radius of 1.8 m. At an instant when the string makes an angle of 40 degrees below the horizontal, the speed of the mass is 5.0 m/s. What is the magnitude of the tension in the string at this instant? Draw the FBD. a. 9.5 N b. 3.0 N c. 8.1 N d. 5.6 N e. 4.7 N
68 Minimum Speed for Vertical Circular Motion What is the minimum speed so that the ball can go in the circle? That is, when T = 0 at the top? At the top: θ = v T = m + gcosθ = 0 R v = gr Minimal Speed to JUST get around the circle only depends on R! ROOT GRRRRRRRR
69 Loop d Loops: Inside the Vertical Loop Minimum Speed to get to the Top. What is the minimum speed so that the car barely make it around the loop the riders are upside down and feel weightless? R = 10.0m
70 QuickCheck 8.11 Loop d Loops: Inside the Vertical Loop A roller coaster car does a loopthe-loop. Which of the free-body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected. Slide 8-82
71 QuickCheck 8.11 Loop d Loops: Inside the Vertical Loop A roller coaster car does a loopthe-loop. Which of the free-body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected. The track is above the car, so the normal force of the track pushes down. Slide 8-83
72 QuickCheck 8.10 Humps in the Road: Outside the Vertical Loop A car that s out of gas coasts over the top of a hill at a steady 20 m/s. Assume air resistance is negligible. Which free-body diagram describes the car at this instant? Slide 8-80
73 QuickCheck 8.10 Humps in the Road: Outside the Vertical Loop A car that s out of gas coasts over the top of a hill at a steady 20 m/s. Assume air resistance is negligible. Which free-body diagram describes the car at this instant? Now the centripetal acceleration points down. Slide 8-81
74 Humps in the Road Outside the Vertical Loop A roller-coaster car has a mass of 500 kg when fully loaded with passengers. The car passes over a hill of radius 15 m, as shown. At the top of the hill, the car has a speed of 8.0 m/s. What is the force of the track on the car at the top of the hill? a. 7.0 kn up b. 7.0 kn down c. 2.8 kn down d. 2.8 kn up e. 5.6 kn down
75 Loop d Loops: Inside the Vertical Loop A roller-coaster car has a mass of 500 kg when fully loaded with passengers. At the bottom of a circular dip of radius 40 m (as shown in the figure) the car has a speed of 16 m/s. What is the magnitude of the force of the track on the car at the bottom of the dip? a. 3.2 kn b. 8.1 kn c. 4.9 kn d. 1.7 kn e. 5.3 kn
76 What is the maximum speed the vehicle can have at B and still remain on the track?
77 Maximum Speed for Vertical Circular Motion Humps in the Road What is the maximum speed the car can have as it passes this highest point without losing contact with the road? : Max speed without losing contact MEANS: n Take : n = 0 Therefore: mg = mv r 2 v = gr mg Maximum Speed to not loose contact with road only depends on R! ROOT GRRRRRRRR
78 Hints for HW Problem Determine the range of speeds a car can have without slipping up or down the road when it is banked AND has friciton. If the car is about to slip down the incline, f is directed up the incline. This would happen at a minimum speed. When the car is about to slip up the incline, f is directed down the incline. This would happen at a maximum speed.
79 What is the maximum speed the vehicle can have at B and still remain on the track?
Chapter 8: Newton s Laws Applied to Circular Motion
Chapter 8: Newton s Laws Applied to Circular Motion Centrifugal Force is Fictitious? F actual = Centripetal Force F fictitious = Centrifugal Force Center FLEEing Centrifugal Force is Fictitious? Center
More informationChapter Six News! DO NOT FORGET We ARE doing Chapter 4 Sections 4 & 5
Chapter Six News! DO NOT FORGET We ARE doing Chapter 4 Sections 4 & 5 CH 4: Uniform Circular Motion The velocity vector is tangent to the path The change in velocity vector is due to the change in direction.
More informationTranslational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work
Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational
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 informationPHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 8 Lecture RANDALL D. KNIGHT Chapter 8. Dynamics II: Motion in a Plane IN THIS CHAPTER, you will learn to solve problems about motion
More informationLecture 10. Example: Friction and Motion
Lecture 10 Goals: Exploit Newton s 3 rd Law in problems with friction Employ Newton s Laws in 2D problems with circular motion Assignment: HW5, (Chapter 7, due 2/24, Wednesday) For Tuesday: Finish reading
More informationChapter 6. Circular Motion and Other Applications of Newton s Laws
Chapter 6 Circular Motion and Other Applications of Newton s Laws Circular Motion Two analysis models using Newton s Laws of Motion have been developed. The models have been applied to linear motion. Newton
More informationName St. Mary's HS AP Physics Circular Motion HW
Name St. Mary's HS AP Physics Circular Motion HW Base your answers to questions 1 and 2 on the following situation. An object weighing 10 N swings at the end of a rope that is 0.72 m long as a simple pendulum.
More informationB) v `2. C) `2v. D) 2v. E) 4v. A) 2p 25. B) p C) 2p. D) 4p. E) 4p 2 25
1. 3. A ball attached to a string is whirled around a horizontal circle of radius r with a tangential velocity v. If the radius is changed to 2r and the magnitude of the centripetal force is doubled the
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 informationPhysics 207 Lecture 10. Lecture 10. Employ Newton s Laws in 2D problems with circular motion
Lecture 10 Goals: Employ Newton s Laws in 2D problems with circular motion Assignment: HW5, (Chapters 8 & 9, due 3/4, Wednesday) For Tuesday: Finish reading Chapter 8, start Chapter 9. Physics 207: Lecture
More informationContents. Objectives Circular Motion Velocity and Acceleration Examples Accelerating Frames Polar Coordinates Recap. Contents
Physics 121 for Majors Today s Class You will see how motion in a circle is mathematically similar to motion in a straight line. You will learn that there is a centripetal acceleration (and force) and
More informationCircular Motion Test Review
Circular Motion Test Review Name: Date: 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration is equal to zero. B) No,
More informationPhysics 111: Mechanics Lecture 9
Physics 111: Mechanics Lecture 9 Bin Chen NJIT Physics Department Circular Motion q 3.4 Motion in a Circle q 5.4 Dynamics of Circular Motion If it weren t for the spinning, all the galaxies would collapse
More informationPHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 8 Lecture RANDALL D. KNIGHT Chapter 8. Dynamics II: Motion in a Plane IN THIS CHAPTER, you will learn to solve problems about motion
More informationFRICTIONAL FORCES. Direction of frictional forces... (not always obvious)... CHAPTER 5 APPLICATIONS OF NEWTON S LAWS
RICTIONAL ORCES CHAPTER 5 APPLICATIONS O NEWTON S LAWS rictional forces Static friction Kinetic friction Centripetal force Centripetal acceleration Loop-the-loop Drag force Terminal velocity Direction
More informationAn object moving in a circle with radius at speed is said to be undergoing.
Circular Motion Study Guide North Allegheny High School Mr. Neff An object moving in a circle with radius at speed is said to be undergoing. In this case, the object is because it is constantly changing
More informationUniform Circular Motion
Uniform Circular Motion Motion in a circle at constant angular speed. ω: angular velocity (rad/s) Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle,
More informationAP C - Webreview ch 7 (part I) Rotation and circular motion
Name: Class: _ Date: _ AP C - Webreview ch 7 (part I) Rotation and circular motion Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2 600 rev/min is equivalent
More informationChapter 8. Dynamics II: Motion in a Plane
Chapter 8. Dynamics II: Motion in a Plane Chapter Goal: To learn how to solve problems about motion in a plane. Slide 8-2 Chapter 8 Preview Slide 8-3 Chapter 8 Preview Slide 8-4 Chapter 8 Preview Slide
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 informationMomentum Review. Lecture 13 Announcements. Multi-step problems: collision followed by something else. Center of Mass
Lecture 13 Announcements 1. While you re waiting for class to start, please fill in the How to use the blueprint equation steps, in your own words.. Exam results: Momentum Review Equations p = mv Conservation
More informationCentripetal force keeps an Rotation and Revolution
Centripetal force keeps an object in circular motion. Which moves faster on a merry-go-round, a horse near the outside rail or one near the inside rail? While a hamster rotates its cage about an axis,
More informationLecture Presentation. Chapter 6 Preview Looking Ahead. Chapter 6 Circular Motion, Orbits, and Gravity
Chapter 6 Preview Looking Ahead Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Text: p. 160 Slide 6-2 Chapter 6 Preview Looking Back: Centripetal Acceleration In Section 3.8, you learned
More informationMultiple Choice (A) (B) (C) (D)
Multiple Choice 1. A ball is fastened to a string and is swung in a vertical circle. When the ball is at the highest point of the circle its velocity and acceleration directions are: (A) (B) (C) (D) 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 informationPhysics 1100: Uniform Circular Motion & Gravity
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Physics 1100: Uniform Circular Motion & Gravity 1. In the diagram below, an object travels over a hill, down a valley, and around a loop the loop at constant
More informationChapter 6 Circular Motion, Orbits and Gravity
Chapter 6 Circular Motion, Orbits and Gravity Topics: The kinematics of uniform circular motion The dynamics of uniform circular motion Circular orbits of satellites Newton s law of gravity Sample question:
More informationChapter 8. Accelerated Circular Motion
Chapter 8 Accelerated Circular Motion 8.1 Rotational Motion and Angular Displacement A new unit, radians, is really useful for angles. Radian measure θ(radians) = s = rθ s (arc length) r (radius) (s in
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 informationUniform Circular Motion. Uniform Circular Motion
Uniform Circular Motion Uniform Circular Motion Uniform Circular Motion An object that moves at uniform speed in a circle of constant radius is said to be in uniform circular motion. Question: Why is uniform
More informationPhysics 201, Lecture 10
Physics 201, Lecture 10 Today s Topics n Circular Motion and Newton s Law (Sect. 6.1,6.2) n Centripetal Force in Uniform Circular Motion n Examples n n Motion in Accelerated Frame (sec. 6.3, conceptual
More informationLecture PowerPoints. Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition. Giancoli
Lecture PowerPoints Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided solely
More informationCircular Orbits. Slide Pearson Education, Inc.
Circular Orbits The figure shows a perfectly smooth, spherical, airless planet with one tower of height h. A projectile is launched parallel to the ground with speed v 0. If v 0 is very small, as in trajectory
More informationRotational Motion and the Law of Gravity 1
Rotational Motion and the Law of Gravity 1 Linear motion is described by position, velocity, and acceleration. Circular motion repeats itself in circles around the axis of rotation Ex. Planets in orbit,
More informationUniform Circular Motion
Slide 1 / 112 Uniform Circular Motion 2009 by Goodman & Zavorotniy Slide 2 / 112 Topics of Uniform Circular Motion (UCM) Kinematics of UCM Click on the topic to go to that section Period, Frequency, and
More informationPSI AP Physics B Circular Motion
PSI AP Physics B Circular Motion Multiple Choice 1. A ball is fastened to a string and is swung in a vertical circle. When the ball is at the highest point of the circle its velocity and acceleration directions
More informationDynamics II Motion in a Plane. Review Problems
Dynamics II Motion in a Plane Review Problems Problem 1 A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N thrust
More informationProficient. a. The gravitational field caused by a. The student is able to approximate a numerical value of the
Unit 6. Circular Motion and Gravitation Name: I have not failed. I've just found 10,000 ways that won't work.-- Thomas Edison Big Idea 1: Objects and systems have properties such as mass and charge. Systems
More informationHonors Assignment - Circular and Periodic Motion
Honors Assignment - Circular and Periodic Motion Reading: Chapter 5, and 11 1 through 11 5 Objectives/HW: Assignment #1 M: # 1 6 Assignment #2 M: # 7 15 Assignment #3 Text: Chap 5 # 6, 12 M: # 17 22 Assignment
More informationIntroductory Physics PHYS101
Introductory Physics PHYS101 Dr Richard H. Cyburt Office Hours Assistant Professor of Physics My office: 402c in the Science Building My phone: (304) 384-6006 My email: rcyburt@concord.edu TRF 9:30-11:00am
More informationAlgebra Based Physics Uniform Circular Motion
1 Algebra Based Physics Uniform Circular Motion 2016 07 20 www.njctl.org 2 Uniform Circular Motion (UCM) Click on the topic to go to that section Period, Frequency and Rotational Velocity Kinematics of
More informationPhysics 2211 ABC Quiz #3 Solutions Spring 2017
Physics 2211 ABC Quiz #3 Solutions Spring 2017 I. (16 points) A block of mass m b is suspended vertically on a ideal cord that then passes through a frictionless hole and is attached to a sphere of mass
More informationphysics Chapter 8 Lecture a strategic approach randall d. knight FOR SCIENTISTS AND ENGINEERS CHAPTER8_LECTURE8.1 THIRD EDITION
Chapter 8 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight CHAPTER8_LECTURE8.1 2013 Pearson Education, Inc. 1 Chapter 8. Newton s Laws for Circular Motion
More informationNo Brain Too Small PHYSICS
MECHANICS: CIRCULAR MOTION QUESTIONS CIRCULAR MOTION (2016;1) Alice is in a car on a ride at a theme park. The car travels along a circular track that is banked, as shown in the diagram. On the diagram,
More informationChapter 5 Review : Circular Motion; Gravitation
Chapter 5 Review : Circular Motion; Gravitation Conceptual Questions 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration
More informationCircular Motion.
1 Circular Motion www.njctl.org 2 Topics of Uniform Circular Motion (UCM) Kinematics of UCM Click on the topic to go to that section Period, Frequency, and Rotational Velocity Dynamics of UCM Vertical
More informationExtension of Circular Motion & Newton s Laws. Chapter 6 Mrs. Warren Kings High School
Extension of Circular Motion & Newton s Laws Chapter 6 Mrs. Warren Kings High chool Review from Chapter 4 Uniform Circular Motion Centripetal Acceleration Uniform Circular Motion, Force F r A force is
More information1D-04 Radial Acceleration & Tangential Velocity
1D-04 Radial Acceleration & Tangential Velocity Once the string is cut, where is the ball going? AT ANY INSTANT, THE VELOCITY VECTOR OF THE BALL IS DIRECTED ALONG THE TANGENT. AT THE INSTANT WHEN THE BLADE
More informationChapter 5 Lecture Notes
Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414 - Strauss Constants: G = 6.67 10-11 N-m 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular
More informationAnnouncements 15 Oct 2013
Announcements 15 Oct 2013 1. While you re waiting for class to start, see how many of these blanks you can fill out. Tangential Accel.: Direction: Causes speed to Causes angular speed to Therefore, causes:
More informationName Period Date A) B) C) D)
Example Problems 9.2 E1. A car rounds a curve of constant radius at a constant speed. Which diagram best represents the directions of both the car s velocity and acceleration? Explain: A) B) C) D) E2.
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 informationCEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5
1 / 40 CEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa 2 / 40 EQUATIONS OF MOTION:RECTANGULAR COORDINATES
More informationMultiple Choice Portion
Unit 5: Circular Motion and Gravitation Please Note that the gravitational potential energy questions are located in Unit 4 (Energy etc.) Multiple Choice Portion 1. What is the centripetal acceleration
More informationThis Week. 2/3/14 Physics 214 Fall
This Week Circular motion Going round the bend Riding in a ferris wheel, the vomit comet Gravitation Our solar system, satellites (Direct TV) The tides, Dark matter, Space Elevator 2/3/14 Physics 214 Fall
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 informationCircular Velocity and Centripetal Acceleration
1. An object is spun around in circular motion such that it completes 100 cycles in 25 s. a. What is the period of its rotation? [0.25 s] b. If the radius is 0.3 m what is the velocity? [7.54 m/s] c. Draw
More informationdt 2 x = r cos(θ) y = r sin(θ) r = x 2 + y 2 tan(θ) = y x A circle = πr 2
v = v i + at a dv dt = d2 x dt 2 A sphere = 4πr 2 x = x i + v i t + 1 2 at2 x = r cos(θ) V sphere = 4 3 πr3 v 2 = v 2 i + 2a x F = ma R = v2 sin(2θ) g y = r sin(θ) r = x 2 + y 2 tan(θ) = y x a c = v2 r
More informationTYPICAL NUMERIC QUESTIONS FOR PHYSICS I REGULAR QUESTIONS TAKEN FROM CUTNELL AND JOHNSON CIRCULAR MOTION CONTENT STANDARD IB
TYPICAL NUMERIC QUESTIONS FOR PHYSICS I REGULAR QUESTIONS TAKEN FROM CUTNELL AND JOHNSON CIRCULAR MOTION CONTENT STANDARD IB 1. A car traveling at 20 m/s rounds a curve so that its centripetal acceleration
More informationHATZIC SECONDARY SCHOOL
HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT CIRCULAR MOTION MULTIPLE CHOICE / 30 OPEN ENDED / 65 TOTAL / 95 NAME: 1. An object travels along a path at constant speed. There is a constant
More informationS Notre Dame 1
Worksheet 1 Horizontal Circular Motion 1. Will the acceleration of a car be the same if it travels Around a sharp curve at 60 km/h as when it travels around a gentle curve at the same speed? Explain. 2.
More informationLinear vs. Rotational Motion
Linear vs. Rotational Motion Every term in a linear equation has a similar term in the analogous rotational equation. Displacements: s = r θ v t ω Speeds: v t = ω r Accelerations: a t = α r Every point
More informationLecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity
Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Suggested Videos for Chapter 6 Prelecture Videos Forces and Apparent Forces Solving Circular Motion Problems Orbits and Gravity Class
More informationEQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5)
EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5) Today s Objectives: Students will be able to apply the equation of motion using normal and tangential coordinates. APPLICATIONS Race
More informationPractice Problems from Chapters 11-13, for Midterm 2. Physics 11a Fall 2010
Practice Problems from Chapters 11-13, for Midterm 2. Physics 11a Fall 2010 Chapter 11 1. The Ferris wheel shown below is turning at constant speed. Draw and label free-body diagrams showing the forces
More informationPage 2. Q1.A satellite X is in a circular orbit of radius r about the centre of a spherical planet of mass
Q1. satellite X is in a circular orbit of radius r about the centre of a spherical planet of mass M. Which line, to, in the table gives correct expressions for the centripetal acceleration a and the speed
More informationWelcome back to Physics 211. Physics 211 Spring 2014 Lecture ask a physicist
Welcome back to Physics 211 Today s agenda: Forces in Circular Motion Impulse Physics 211 Spring 2014 Lecture 07-1 1 ask a physicist My question is on sonoluminescence, which is supposed to be when a sound
More informationCircular Motion Dynamics
Circular Motion Dynamics 8.01 W04D2 Today s Reading Assignment: MIT 8.01 Course Notes Chapter 9 Circular Motion Dynamics Sections 9.1-9.2 Announcements Problem Set 3 due Week 5 Tuesday at 9 pm in box outside
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 informationA Level. A Level Physics. Circular Motion (Answers) Edexcel. Name: Total Marks: /30
Visit http://www.mathsmadeeasy.co.uk/ for more fantastic resources. Edexcel A Level A Level Physics Circular Motion (Answers) Name: Total Marks: /30 Maths Made Easy Complete Tuition Ltd 2017 1. Total for
More informationPhysics 20 Practice Problems for Exam 1 Fall 2014
Physics 20 Practice Problems for Exam 1 Fall 2014 Multiple Choice Short Questions (1 pt ea.) Circle the best answer. 1. An apple falls from a tree and hits the ground 5 meters below. It hits the ground
More informationExperiment #7 Centripetal Force Pre-lab Questions Hints
Experiment #7 Centripetal Force Pre-lab Questions Hints The following are some hints for this pre-lab, since a few of these questions can be a little difficult. Note that these are not necessarily the
More informationChapter 8. Centripetal Force and The Law of Gravity
Chapter 8 Centripetal Force and The Law of Gravity Centripetal Acceleration An object traveling in a circle, even though it moves with a constant speed, will have an acceleration The centripetal acceleration
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 informationThings going in circles
Things going in circles Physics 211 Syracuse University, Physics 211 Spring 2019 Walter Freeman February 18, 2019 W. Freeman Things going in circles February 18, 2019 1 / 30 Announcements Homework 4 due
More information4 th week of Lectures Jan. 29. Feb
4 th week of Lectures Jan. 29. Feb. 02. 2018. Circular motion Going around the bend Riding in a Ferris wheel Gravitation Our solar system, satellites The tides 1/31/2018 Physics 214 Spring 2018 1 The Greatest
More informationAP Physics 1 Lesson 9 Homework Outcomes. Name
AP Physics 1 Lesson 9 Homework Outcomes Name Date 1. Define uniform circular motion. 2. Determine the tangential velocity of an object moving with uniform circular motion. 3. Determine the centripetal
More information(b) The period T and the angular frequency ω of uniform rotation are related to the cyclic frequency f as. , ω = 2πf =
PHY 302 K. Solutions for problem set #9. Non-textbook problem #1: (a) Rotation frequency of 1 Hz means one revolution per second, or 60 revolutions per minute (RPM). The pre-lp vinyl disks rotated at 78
More informationQuest Chapter 09. Eliminate the obviously wrong answers. Consider what is changing: speed, velocity, some part of velocity? Choose carefully.
1 A dragster maintains a speedometer reading of 100 km/h and passes through a curve with a constant radius. Which statement is true? 1. The dragster rounded the curve at a changing speed of 100 km/h. 2.
More informationCircular Motion & Gravitation MC Question Database
(Questions #4,5,6,27,37,38,42 and 58 each have TWO correct answers.) 1) A record player has four coins at different distances from the center of rotation. Coin A is 1 cm away, Coin B is 2 cm away. Coin
More informationPH 2213 : Chapter 05 Homework Solutions
PH 2213 : Chapter 05 Homework Solutions Problem 5.4 : The coefficient of static friction between hard rubber and normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave
More informationΣF=ma SECOND LAW. Make a freebody diagram for EVERY problem!
PHYSICS HOMEWORK #31 SECOND LAW ΣF=ma NEWTON S LAWS Newton s Second Law of Motion The acceleration of an object is directly proportional to the force applied, inversely proportional to the mass of the
More information= o + t = ot + ½ t 2 = o + 2
Chapters 8-9 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 informationDynamics Test K/U 28 T/I 16 C 26 A 30
Name: Dynamics Test K/U 28 T/I 16 C 26 A 30 A. True/False Indicate whether the sentence or statement is true or false. 1. The normal force that acts on an object is always equal in magnitude and opposite
More informationExam Question 6/8 (HL/OL): Circular and Simple Harmonic Motion. February 1, Applied Mathematics: Lecture 7. Brendan Williamson.
in a : Exam Question 6/8 (HL/OL): Circular and February 1, 2017 in a This lecture pertains to material relevant to question 6 of the paper, and question 8 of the Ordinary Level paper, commonly referred
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 informationAP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force).
AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force). 1981M1. A block of mass m, acted on by a force of magnitude F directed horizontally to the
More information(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m
PSI AP Physics C Work and Energy (Algebra Based) Multiple Choice Questions (use g = 10 m/s 2 ) 1. A student throws a ball upwards from the ground level where gravitational potential energy is zero. At
More informationa reference frame that accelerates in a straight line a reference frame that moves along a circular path Straight Line Accelerated Motion
1.12.1 Introduction Go back to lesson 9 and provide bullet #3 In today s lesson we will consider two examples of non-inertial reference frames: a reference frame that accelerates in a straight line a reference
More information4) Vector = and vector = What is vector = +? A) B) C) D) E)
1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In
More informationCircular Motion and Gravitation. Centripetal Acceleration
Circular Motion and Gravitation Centripetal Acceleration Recall linear acceleration 3. Going around a curve, at constant speed 1. Speeding up vi vi Δv a ac ac vi ac 2. Slowing down v velocity and acceleration
More informationChapter 4 Circular Motion and Gravitation Planetary Data Homework # 26
Planetary Data Homework # 26 PLANETARY DATA Mean Distance Mass from Sun Radius Period Planet (kg) (m) (m) (days) Sun 1.99 x 10 30 6.970 x 10 8 Mercury 3.30 x 10 23 5.791 x 10 10 2.439 x 10 6 87.97 Venus
More informationCircular Motion and Gravitation. Centripetal Acceleration
Circular Motion and Gravitation Centripetal Acceleration Recall linear acceleration! Δv! aavg t 3. Going around urve, at constant speed 1. Speeding up vi vi Δv a ac ac vi ac. Slowing down v velocity and
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) You are standing in a moving bus, facing forward, and you suddenly fall forward as the
More informationCircular Motion & Rotational Mechanics. Semester 2 Review Project - Sonya Kalara, Ellie Kim, and Charlotte Spry
Circular Motion & Rotational Mechanics Semester 2 Review Project - Sonya Kalara, Ellie Kim, and Charlotte Spry Definitions II. III. IV. I. Uniform Circular Motion - an object that moves in a circle at
More informationPractice Exam 2. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: _ Practice Exam 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A roller-coaster car has a mass of 500 kg when fully loaded with passengers.
More informationCHAPTER 7 CIRCULAR MOTION
CHAPTER 7 CIRCULAR MOTION 1 Describing Circular Motion Picture of Uniform Circular Motion Is the object accelerating? Linear speed vs Angular Speed Period of Rotation Page 1 2 Centripetal Acceleration
More informationExam 1 Solutions. Kinematics and Newton s laws of motion
Exam 1 Solutions Kinematics and Newton s laws of motion No. of Students 80 70 60 50 40 30 20 10 0 PHY231 Spring 2012 Midterm Exam 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Raw Score 1. In which
More informationThis Week. 7/29/2010 Physics 214 Fall
This Week Circular motion Going round the bend Riding in a ferris wheel, the vomit comet Gravitation Our solar system, satellites (Direct TV) The tides, Dark matter, Space Elevator 7/29/2010 Physics 214
More information