Physics. Chapter 8 Rotational Motion

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Physics. Chapter 8 Rotational Motion"

Transcription

1 Physics Chapter 8 Rotational Motion

2 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 per unit of time. Symbol is omega, ω and units are RPM (rotations per minute)

3 Circular Motion Does tangential speed depend on where the bug sits on the record? Does rotational speed depend on where the bug sits on the record?

4 Circular Motion Is there a relationship between v and ω? v ~ r ω Question: Who is moving at a greater tangential speed: someone at the equator or someone in Winchester, Virginia?

5 Circular Motion

6 Check Question At an amusement park, you and a friend sit on a large rotating disk. You sit at the edge and have a rotational speed of 4 RPM and a linear speed of 6 m/s. Your friend sits halfway to the center. What is her rotational speed? What is her linear speed?

7 Wheels on Trains

8 Period and Frequency All objects undergoing circular motion have one thing in common - they return to the same location every time they complete one cycle (one circumference). The time to complete one cycle is called the Period, T. T = t number of cycles ** Units seconds

9 Period and Frequency The frequency, f, of an object is the number of cycles an object completes during one second. In other words, how frequently, the object is cycling. Frequency is the inverse of Period. f = number of cycles 1 = t T ** Units cycles per second = Hertz

10 Check Question An object completes 20 revolutions in 10 seconds. Determine period and frequency of this motion.

11 Tangential Velocity Velocity involves both speed and direction. When an object moves in a circle, even at constant speed, the object still undergoes acceleration because its direction is changing. Several instantaneous velocity vectors are drawn in - notice they are all TANGENT to the circle.

12 Tangential Velocity We can calculate the magnitude of the tangential velocity as follows: d v = = t 2π r T

13 Centripetal Acceleration Since the direction of v is constantly changing for a circling object, we know it is continuously accelerating. This type of acceleration is called centripetal acceleration, a c. Centripetal acceleration is always directed toward the center of the circle.

14 Centripetal Acceleration We can calculate centripetal acceleration as follows: a c = v 2 r

15 Check Question Determine the acceleration of an object experiencing uniform circular motion. It is moving in a circle with a radius of 10 meters and a frequency of 0.25 Hertz.

16 Centripetal Force Recall that the cause of any acceleration is a force. In uniform circular motion, the net force is known as the centripetal force. From Newton s second law: F c = ma c = mv 2 r The centripetal force acts in the SAME direction as the centripetal acceleration.

17 Check Question - Horizontal Circular Motion A racing car is speeding around a flat, unbanked circular track whose radius is 250 meters. The car s speed is a constant 50.0 meters per second. The mass of the car is 2.00 x 103 kg. What provides the centripetal force necessary to keep the car in its circular path? Calculate the magnitude of the centripetal force in newtons on the car.

18 Centripetal Force Centripetal force holds a car in a curved path. a. For the car to go around a curve, there must be sufficient friction to provide the required centripetal force. b. If the force of friction is not great enough, skidding occurs.

19 Check Question - Horizontal Circular Motion A car moving at 10 meters / second completes a turn with a radius of 20 meters. Determine the minimum coefficient of friction between the tires and the road that will allow the car to complete the turn without skidding.

20 Check Question - Horizontal Circular Motion A mass m is in uniform circular motion with a speed v and a radius r. How is the centripetal acceleration affected if the radius is doubled while the speed remains constant?

21 Check Question - Vertical Circular Motion Imagine an ideal pendulum bob weighing 2.0 kg and swinging back and forth. At its lowest point (rest position) it has velocity 10 m/s. If the length of the pendulum string is 10 meters, what is the centripetal force on the pendulum bob at its lowest point?

22 Check Question - Vertical Circular Motion A 2.0-kilogram mass is attached to the end of a 1.0-meterlong string. When the apparatus is swung in a vertical circle, the mass reaches a speed of 10 meters per second at the bottom of the swing. A. Determine the tension in the string at the bottom of the swing. B. Determine the minimum speed at the top of the loop that allows the mass to make one complete cycle.

23 Check Question - Vertical Circular Motion A roller coaster loop has a radius of 10.0 meters. What minimum speed is required at the top of the loop in order to complete the loop successfully?

24 Centripetal Force

25 Calculating Centripetal Force c

26 Centripetal Force F v

27 Centripetal Force The clothes in a washing machine are forced into a circular path, but the water is not, and it flies off tangentially.

28 Centripetal Force T T y T x

29 Conical Pendulum

30 Banked Curves

31 Centrifugal Force

32 Centrifugal Force Effect The centrifugal-force effect is attributed not to any real force but to inertia the tendency of the moving body to follow a straight-line path.

33 Centrifugal vs Centripetal Force If the string on the can were to break, would the can move outward? No, because there is no outward force acting on it. It would move off in a straight line tangent to its location at the moment the string broke.

34 Check Question A heavy iron ball is attached by a spring to a rotating platform, as shown in the sketch. Two observers, one in the rotating frame and one on the ground at rest, observe its motion. Which observer sees the ball being pulled outward, stretching the spring? Which observer sees the spring pulling the ball into circular motion?

35 Check Question Mass m is positioned 1.0 meter from the center of a circular disk that is rotating with increasing speed, as shown bleow. The coefficient of friction between the mass and the disk is What maximum speed can the mass obtain before it slips off the rotating disk?

36 Simulated Gravity From within a rotating frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.

37 Simulated Gravity The man inside this rotating space habitat experiences simulated gravity. As seen from the outside, the only force exerted on the man is by the floor. As seen from the inside, there is a fictitious centrifugal force that simulates gravity.

38 Challenges of Simulated Gravity The magnitude of the centripetal/centrifugal force is directly proportional to the radial distance. Human sensitivity to rotation. Large structure required

39 Rotational Inertia An object rotating about an axis tends to remain rotating about the same axis unless interfered with by some external influence. The greater the distance between an object s mass concentration and the axis, the greater the rotational inertia.

40 Rotational Inertia

41 Rotational Inertia So how can we calculate rotational inertia? I = mr 2 ONLY for the case where all the mass, m, is concentrated at the same distance, r, from a rotational axis. When the mass is more spread out, the rotational inertia is less and the formula is different.

42 Rotational Inertia

43 Rotational Inertia Which will roll down an incline with greater acceleration, a hollow cylinder or a solid cylinder of the same mass and radius?

44 Rotational Inertia It turns out that any solid cylinder will roll down an incline with more acceleration than any hollow cylinder, regardless of mass or radius. A hollow cylinder has more laziness per mass than a solid cylinder.

45 Check Question A heavy iron cylinder and a light wooden cylinder, similar in shape, roll down an incline. Which will have more acceleration? The cylinders have different masses, but the same rotational inertia per mass, so both will accelerate equally down the incline. Their different masses make no difference, just as the acceleration of free fall is not affected by different masses. All objects of the same shape have the same laziness per mass ratio.

46 Rotational Inertia Rotational inertia can be used to advantage. Industrial flywheels

47 Torque Torque is the rotational counterpart to Force Apply a force if you want linear motion (acceleration) Apply a torque if you want rotation.

48 Torque Now we have to expand our definition of Mechanical Equilibrium! F = 0 AND τ = 0

49 Torque Let s consider a door:

50 Torque When the force is perpendicular, the distance from the turning axis to the point of contact is called the lever arm.

51 Torque The same torque can be produced by a large force with a short lever arm, or a small force with a long lever arm.

52 Check Question If you cannot exert enough torque to turn a stubborn bolt, would more torque be produced if you fastened a length of rope to the wrench handle as shown?

53 Check Question

54 Balanced Torques A pair of torques can balance each other. Balance is achieved if the torque that tends to produce clockwise rotation by the boy equals the torque that tends to produce counterclockwise rotation by the girl.

55 Check Question This meter stick is suspended in mechanical equilibrium. What is the weight of the block hanging at the 10 cm mark?

56 Balanced Torques Scale balances that work with sliding weights are based on balanced torques, not balanced masses. The sliding weights are adjusted until the counterclockwise torque just balances the clockwise torque. We say the scale is in rotational equilibrium.

57 Center of Mass A baseball thrown into the air follows a smooth parabolic path.

58 Center of Mass A bat thrown in the air, however, wobbles about a special point. This point stays on a parabolic path, even though the rest of the bat does not. This point, called the center of mass, is where all the mass of an object can be considered to be concentrated.

59 Center of Mass Center of Mass is the average position of all mass that makes up the object Center of Gravity is the average position of all the particles of weight that make up an object

60 Center of Mass Location of the Center of Mass

61 Center of Mass Objects not made of the same material throughout may have the center of mass quite far from the geometric center. Consider a hollow ball half filled with lead. The center of mass would be located somewhere within the lead part. The ball will always roll to a stop with its center of mass as low as possible.

62 Center of Mass Motion About the Center of Mass As an object slides across a surface, its center of mass follows a straight-line path.

63 Spin A force must be applied to the edge of an object for it to spin. a. If the football is kicked in line with its center, it will move without rotating. b. If it is kicked above or below its center, it will rotate.

64 Center of Gravity So how can we precisely locate the center of gravity (CG)? The CG of a uniform object is at the midpoint, its geometric center. The CG is the balance point. Supporting that single point supports the whole object.

65 Center of Gravity The CG of an object may be located where no actual material exists. The CG of a ring lies at the geometric center where no matter exists. The same holds true for a hollow sphere such as a basketball.

66 Check Question A Uniform meterstick supported at the 25-cm mark balances when a 1 kg rock is suspended at the 0-cm end. What is the mass of the meterstick?

67 Torque & Center of Gravity

68 Torque & Center of Gravity

69 Torque & Center of Gravity The Leaning Tower of Pisa does not topple because its CG does not extend beyond its base.

70 Center of Gravity

71 Balancing Question: Which way do you suppose it will be easier to balance a baseball bat on your finger?

72 Stability The CG of a building is lowered if much of the structure is below ground level. This is important for tall, narrow structures.

73 Spools

74 Angular Momentum Anything that rotates keeps on rotating until something stops it. Recall what we learned about linear momentum: P = linear inertia x linear velocity = m x v Angular momentum is defined as the product of rotational inertia, I, and rotational velocity, ω. angular momentum = rotational inertia rotational velocity

75 Angular Momentum Angular momentum depends on rotational velocity and rotational inertia. The operation of a gyroscope relies on the vector nature of angular momentum.

76 Angular Momentum Just as an external net force is required to change the linear momentum of an object. An external net torque is required to change the angular momentum of an object. An object or system of objects will maintain its angular momentum unless acted upon by an external net torque.

77 Conservation of Angular Momentum Angular momentum is conserved for systems in rotation. The law of conservation of angular momentum states that if no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant. With no external torque, the product of rotational inertia and rotational velocity at one time will be the same as at any other time.

78 Conservation of Angular Momentum When the man pulls his arms and the whirling weights inward, he decreases his rotational inertia, and his rotational speed correspondingly increases.

79 Conservation of Angular Momentum Rotational speed is controlled by variations in the body s rotational inertia as angular momentum is conserved during a forward somersault. This is done by moving some part of the body toward or away from the axis of rotation.

Centripetal force keeps an object in circular motion Rotation and Revolution

Centripetal force keeps an object in circular motion Rotation and Revolution Centripetal force keeps an object in circular motion. 10.1 Rotation and Revolution Two types of circular motion are and. An is the straight line around which rotation takes place. When an object turns

More information

Centripetal force keeps an Rotation and Revolution

Centripetal 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 information

Chapter 8: Rotational Motion

Chapter 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 information

Circular Motion Tangential Speed. Conceptual Physics 11 th Edition. Circular Motion Rotational Speed. Circular Motion

Circular 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 information

Angular Motion Unit Exam Practice

Angular 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 information

In the absence of an external force, the momentum of an object remains unchanged conservation of momentum. In this. rotating objects tend to

In the absence of an external force, the momentum of an object remains unchanged conservation of momentum. In this. rotating objects tend to Rotating objects tend to keep rotating while non- rotating objects tend to remain non-rotating. In the absence of an external force, the momentum of an object remains unchanged conservation of momentum.

More information

Circular Motion.

Circular 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 information

Rotational Mechanics Part III Dynamics. Pre AP Physics

Rotational 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 information

Name St. Mary's HS AP Physics Circular Motion HW

Name 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 information

Circular Motion. Conceptual Physics 11 th Edition. Circular Motion Tangential Speed

Circular Motion. Conceptual Physics 11 th Edition. Circular Motion Tangential Speed Conceptual Physics 11 th Edition Circular Motion Rotational Inertia Torque Center of Mass and Center of Gravity Centripetal Force Centrifugal Force Chapter 8: ROTATION Rotating Reference Frames Simulated

More information

Lecture 3. Rotational motion and Oscillation 06 September 2018

Lecture 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 information

Chapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction

Chapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction 1. The distance between a turning axis and the

More information

AP Physics 1 Lesson 9 Homework Outcomes. Name

AP 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) v `2. C) `2v. D) 2v. E) 4v. A) 2p 25. B) p C) 2p. D) 4p. E) 4p 2 25

B) 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 information

CHAPTER 8 TEST REVIEW MARKSCHEME

CHAPTER 8 TEST REVIEW MARKSCHEME AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM

More information

Test 7 wersja angielska

Test 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 information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE 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 information

Concept Question: Normal Force

Concept 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 information

AP Physics Free Response Practice Dynamics

AP Physics Free Response Practice Dynamics AP Physics Free Response Practice Dynamics 14) In the system shown above, the block of mass M 1 is on a rough horizontal table. The string that attaches it to the block of mass M 2 passes over a frictionless

More information

Uniform Circular Motion

Uniform 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 information

Circular motion, Center of Gravity, and Rotational Mechanics

Circular motion, Center of Gravity, and Rotational Mechanics Circular motion, Center of Gravity, and Rotational Mechanics Rotation and Revolution Every object moving in a circle turns around an axis. If the axis is internal to the object (inside) then it is called

More information

Period: Date: Review - UCM & Energy. Page 1. Base your answers to questions 1 and 2 on the information and diagram below.

Period: Date: Review - UCM & Energy. Page 1. Base your answers to questions 1 and 2 on the information and diagram below. Base your answers to questions 1 and 2 on the information and diagram below. The diagram shows the top view of a -kilogram student at point A on an amusement park ride. The ride spins the student in a

More information

Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS

Name 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 information

Mechanics II. Which of the following relations among the forces W, k, N, and F must be true?

Mechanics II. Which of the following relations among the forces W, k, N, and F must be true? Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which

More information

Name Period Date A) B) C) D)

Name 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 information

5. A car moves with a constant speed in a clockwise direction around a circular path of radius r, as represented in the diagram above.

5. A car moves with a constant speed in a clockwise direction around a circular path of radius r, as represented in the diagram above. 1. The magnitude of the gravitational force between two objects is 20. Newtons. If the mass of each object were doubled, the magnitude of the gravitational force between the objects would be A) 5.0 N B)

More information

Chapter 8 Rotational Motion

Chapter 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 information

Chapter 8, Rotational Equilibrium and Rotational Dynamics. 3. If a net torque is applied to an object, that object will experience:

Chapter 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 information

PHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS. 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 information

Slide 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?

Slide 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 information

Slide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133

Slide 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 information

Rotation. PHYS 101 Previous Exam Problems CHAPTER

Rotation. 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 information

1. In which situation is an object undergoing centripetal acceleration? (C) a car accelerating on a drag strip (D) a hockey puck gliding on ice

1. In which situation is an object undergoing centripetal acceleration? (C) a car accelerating on a drag strip (D) a hockey puck gliding on ice Physics 3204 Assignment 2.1 UCM DUE: Thursday Nov 24, 2017 Name: Part A. Multiple Choice: Select the best possible answer. Place the answer on the answer sheet. 1. In which situation is an object undergoing

More information

Kinematics. v (m/s) ii. Plot the velocity as a function of time on the following graph.

Kinematics. v (m/s) ii. Plot the velocity as a function of time on the following graph. Kinematics 1993B1 (modified) A student stands in an elevator and records his acceleration as a function of time. The data are shown in the graph above. At time t = 0, the elevator is at displacement x

More information

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.

6. 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 information

Algebra Based Physics Uniform Circular Motion

Algebra 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 information

We define angular displacement, θ, and angular velocity, ω. What's a radian?

We 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 information

AP practice ch 7-8 Multiple Choice

AP practice ch 7-8 Multiple Choice AP practice ch 7-8 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 information

An object moving in a circle with radius at speed is said to be undergoing.

An 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 information

Page 1. Name:

Page 1. Name: Name: 3834-1 - Page 1 1) If a woman runs 100 meters north and then 70 meters south, her total displacement is A) 170 m south B) 170 m north C) 30 m south D) 30 m north 2) The graph below represents the

More information

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular

Big 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 information

PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion PSI AP Physics I Rotational Motion Multiple-Choice 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 information

AP Physics 1: Rotational Motion & Dynamics: Problem Set

AP 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 information

Chapter 9-10 Test Review

Chapter 9-10 Test Review Chapter 9-10 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

Use the following to answer question 1:

Use 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 information

HATZIC SECONDARY SCHOOL

HATZIC 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 information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE 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) Horses with the greatest linear speed on a merry-go-round are located 1) A) near the

More information

Vocabulary. Centripetal Force. Centripetal Acceleration. Rotate. Revolve. Linear Speed. Angular Speed. Center of Gravity. 1 Page

Vocabulary. Centripetal Force. Centripetal Acceleration. Rotate. Revolve. Linear Speed. Angular Speed. Center of Gravity. 1 Page Vocabulary Term Centripetal Force Definition Centripetal Acceleration Rotate Revolve Linear Speed Angular Speed Center of Gravity 1 Page Force Relationships 1. FORCE AND MASS a. An object swung in a uniform

More information

= o + t = ot + ½ t 2 = o + 2

= 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 information

Chapter 8. Dynamics II: Motion in a Plane

Chapter 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 information

PHY2020 Test 2 November 5, Name:

PHY2020 Test 2 November 5, Name: 1 PHY2020 Test 2 November 5, 2014 Name: sin(30) = 1/2 cos(30) = 3/2 tan(30) = 3/3 sin(60) = 3/2 cos(60) = 1/2 tan(60) = 3 sin(45) = cos(45) = 2/2 tan(45) = 1 sin(37) = cos(53) = 0.6 cos(37) = sin(53) =

More information

Today. Ch. 8 on Rotation. Note, all lectures and pre-lectures posted up as always at

Today. Ch. 8 on Rotation. Note, all lectures and pre-lectures posted up as always at Ch. 8 on Rotation Today Note, all lectures and pre-lectures posted up as always at http://www.hunter.cuny.edu/physics/courses/physics100/spring-2016 Looking ahead: Sep 27, Review (Chs 2,3,4,5,6,7,8) Sep

More information

It 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

It 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 information

Chapter 8 - Rotational Dynamics and Equilibrium REVIEW

Chapter 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 information

Proficient. a. The gravitational field caused by a. The student is able to approximate a numerical value of the

Proficient. 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 information

PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion PSI AP Physics I Rotational Motion Multiple-Choice 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 information

Lecture 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. 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 information

AP C - Webreview ch 7 (part I) Rotation and circular motion

AP 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 information

Lecture Presentation Chapter 7 Rotational Motion

Lecture 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 information

Chapter 8 Lecture Notes

Chapter 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 information

UCM-Circular Motion. Base your answers to questions 1 and 2 on the information and diagram below.

UCM-Circular Motion. Base your answers to questions 1 and 2 on the information and diagram below. Base your answers to questions 1 and 2 on the information and diagram The diagram shows the top view of a 65-kilogram student at point A on an amusement park ride. The ride spins the student in a horizontal

More information

Physics 12. Unit 5 Circular Motion and Gravitation Part 1

Physics 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 information

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation Circular Motion and Gravitation Section 1 Preview Section 1 Circular Motion Section 2 Newton s Law of Universal Gravitation Section 3 Motion in Space Section 4 Torque and Simple Machines Circular Motion

More information

Circular Motion CENTRIPETAL ACCELERATION. tf-t,

Circular Motion CENTRIPETAL ACCELERATION. tf-t, Circular Motion Ill SECTION OBJECTIVES Solve problems involving centripetal acceleration. Solve problems involving centripetal force. Explain how the apparent existence of an outward force in circular

More information

3. 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?

3. 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 information

1. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown? [Neglect the effect of

1. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown? [Neglect the effect of 1. A baseball player throws a ball horizontally. Which statement best describes the ball's motion after it is thrown? [Neglect the effect of friction.] A) Its vertical speed remains the same, and its horizontal

More information

UNIT HW ROTATION ANSWER KEY

UNIT HW ROTATION ANSWER KEY Conceptual Questions UNIT HW ROTATION ANSWER KEY 1) D_What type of linear acceleration does an object moving with constant linear speed (st) in a circular path experience? A) free fall C) linear acceleration

More information

In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion.

In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion. 1 PHYS:100 LECTURE 9 MECHANICS (8) In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion. 9 1. Conservation of Energy. Energy is one of the most fundamental

More information

Rotational Dynamics. Slide 2 / 34. Slide 1 / 34. Slide 4 / 34. Slide 3 / 34. Slide 6 / 34. Slide 5 / 34. Moment of Inertia. Parallel Axis Theorem

Rotational Dynamics. Slide 2 / 34. Slide 1 / 34. Slide 4 / 34. Slide 3 / 34. Slide 6 / 34. Slide 5 / 34. Moment of Inertia. Parallel Axis Theorem Slide 1 / 34 Rotational ynamics l Slide 2 / 34 Moment of Inertia To determine the moment of inertia we divide the object into tiny masses of m i a distance r i from the center. is the sum of all the tiny

More information

End-of-Chapter Exercises

End-of-Chapter Exercises End-of-Chapter 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 information

Advanced Higher Physics. Rotational motion

Advanced 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 information

Uniform Circular Motion AP

Uniform Circular Motion AP Uniform Circular Motion AP Uniform circular motion is motion in a circle at the same speed Speed is constant, velocity direction changes the speed of an object moving in a circle is given by v circumference

More information

End-of-Chapter Exercises

End-of-Chapter Exercises End-of-Chapter 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 information

Uniform Circular Motion. Uniform Circular Motion

Uniform 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 information

Recap I. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration:

Recap I. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration: Recap I Angular position: Angular displacement: s Angular velocity: Angular Acceleration: Every point on a rotating rigid object has the same angular, but not the same linear motion! Recap II Circular

More information

Uniform Circular Motion

Uniform 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 information

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics

Circular 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 information

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation Circular Motion and Gravitation Section 1 Preview Section 1 Circular Motion Section 2 Newton s Law of Universal Gravitation Section 3 Motion in Space Section 4 Torque and Simple Machines Circular Motion

More information

CIRCULAR MOTION AND ROTATION

CIRCULAR MOTION AND ROTATION 1. UNIFORM CIRCULAR MOTION So far we have learned a great deal about linear motion. This section addresses rotational motion. The simplest kind of rotational motion is an object moving in a perfect circle

More information

Physics 11 Fall 2012 Practice Problems 6

Physics 11 Fall 2012 Practice Problems 6 Physics 11 Fall 2012 Practice Problems 6 1. Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on

More information

Circular 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 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 information

Cutnell/Johnson Physics

Cutnell/Johnson Physics Cutnell/Johnson Physics Classroom Response System Questions Chapter 5 Dynamics of Uniform Circular Motion Interactive Lecture Questions 5.1.1. An airplane flying at 115 m/s due east makes a gradual turn

More information

Circular Motion. Unit 7

Circular Motion. Unit 7 Circular Motion Unit 7 Do Now You drive a car that follows a circular path with the radius r = 100 m. Find the distance travelled if you made one complete circle. C 2 R 2(3.14)(100) 6.28(100) 628m Uniform

More information

Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs.

Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs. Agenda Today: Homework quiz, moment of inertia and torque Thursday: Statics problems revisited, rolling motion Reading: Start Chapter 8 in the reading Have to cancel office hours today: will have extra

More information

Chapter 9. Rotational Dynamics

Chapter 9. Rotational Dynamics Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

More information

Dynamics Test K/U 28 T/I 16 C 26 A 30

Dynamics 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 information

Projectile and Circular Motion Review Packet

Projectile and Circular Motion Review Packet Conceptual Physics Projectile and Circular Motion Review Packet Mr. Zimmerman Textbook Reference: pp. 33-42, 122-135 Key Terms (fill in definitions) projectile - any object that moves through the air or

More information

Quantitative Skills in AP Physics 1

Quantitative 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

Rotational Motion Examples:

Rotational Motion Examples: Rotational Motion Examples: 1. A 60. cm diameter wheel rotates through 50. rad. a. What distance will it move? b. How many times will the wheel rotate in this time? 2. A saw blade is spinning at 2000.

More information

Rotational Dynamics, Moment of Inertia and Angular Momentum

Rotational 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 information

Chapter 8. Rotational Equilibrium and Rotational Dynamics

Chapter 8. Rotational Equilibrium and Rotational Dynamics Chapter 8 Rotational Equilibrium and Rotational Dynamics 1 Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related 2 Torque The door is free to rotate

More information

Circular Motion PreTest

Circular Motion PreTest Circular Motion PreTest Date: 06/03/2008 Version #: 0 Name: 1. In a series of test runs, a car travels around the same circular track at different velocities. Which graph best shows the relationship between

More information

Circular Orbits. Slide Pearson Education, Inc.

Circular 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 information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #2 November 15, 2001 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION

More information

PSI AP Physics B Circular Motion

PSI 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 information

Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart

Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart Rotational Motion & Angular Momentum Rotational Motion Every quantity that we have studied with translational motion has a rotational counterpart TRANSLATIONAL ROTATIONAL Displacement x Angular Displacement

More information

Chapter 10. Rotation

Chapter 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 MFMcGraw-PHY 45 Chap_10Ha-Rotation-Revised

More information