Physics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here.

Size: px
Start display at page:

Download "Physics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here."

Transcription

1 Physics 07: Lecture 4 Announcements No labs next week, May 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here Today s Agenda ecap: otational dynamics and torque Work and energy with example Many body dynamics examples Weight and massive pulley olling and sliding examples otation around a moving axis: Puck on ice olling down an incline Bowling ball: sliding to rolling Atwood s Machine with a massive pulley 1 eview: Torque and Angular Acceleration τ NET = Iα This is the rotational analogue of NET = ma Torque is the rotational analogue of force: The amount of twist provided by a force. Moment of inertia I is the rotational analogue of mass If I is big, more torque is required to achieve a given angular acceleration. Page 1

2 Torque ecall the definition of torque: τ = r θ = r sin φ = r sin φ r φ φ τ = r p θ r p = distance of closest approach r φ Equivalent definitions! r p 3 Torque τ = r sin φ So if φ = 0 o, then τ = 0 r And if φ = 90 o, then τ = maximum r 4 Page

3 Lecture 3, Act 3 Torque In which of the cases shown below is the torque provided by the applied force about the rotation axis biggest? In both cases the magnitude and direction of the applied force is the same. (a) case 1 (b) case (c) same L axis L case 1 case 5 Lecture 3, Act 3 Solution Torque = x (distance of closest approach) The applied force is the same. The distance of closest approach is the same. Torque is the same! L L case 1 case 6 Page 3

4 Torque and the ight Hand ule: The right hand rule can tell you the direction of torque: Point your hand along the direction from the axis to the point where the force is applied. Curl your fingers in the direction of the force. Your thumb will point in the direction of the torque. y z τ x r 7 The Cross Product We can describe the vectorial nature of torque in a compact form by introducing the cross product. The cross product of two vectors is a third vector: A X B = C B The length of C is given by: C = AB sin φ φ A The direction of C is perpendicular to the plane defined by A and B, and in the direction defined by the right hand rule. C 8 Page 4

5 The Cross Product Cartesian components of the cross product: C = A X B B C X = A Y B Z -B Y A Z C Y = A Z B X -B Z A X A C Z = A X B Y -B X A Y C Note: B X A = - A X B 9 Torque & the Cross Product: So we can define torque as: τ = r X = r sin φ τ X = r Y Z - Y r Z = y Z - Y z τ Y = r Z X - Z r X = z X - Z x τ Z = r X Y - X r Y = x Y - X y τ r y z x 10 Page 5

6 Comment on τ = Iα When we write τ = Iα we are really talking about the z component of a more general vector equation. (ecall that we normally choose the z-axis to be the the rotation axis.) τ z = I z α z τ z z I z We usually omit the z subscript for simplicity. α z 11 Example To loosen a stuck nut, a (stupid) man pulls at an angle of 45 o on the end of a 50 cm wrench with a force of 00 N. What is the magnitude of the torque on the nut? If the nut suddenly turns freely, what is the angular acceleration of the wrench? (The wrench has a mass of 3 kg, and its shape is that of a thin rod). 45 o = 00 N L = 0.5 m 1 Page 6

7 Example Torque τ = Lsin φ = (0.5 m)(00 N)(sin 45) = 70.7 Nm If the nut turns freely, τ = Iα We know τ and we want α, so we need to figure out I. 1 1 I = ML = = 3 3 ( 3 kg)( 0. 5 m) 0. 5 kgm = 00 N 45 o So α = τ / I = (70.7 Nm) / (0.5 kgm ) L = 0.5m α = 83 rad/s α 13 Work Consider the work done by a force acting on an object constrained to move around a fixed axis. or an infinitesimal angular displacement dθ: dw =. dr = dθ cos(β) = dθ cos(90-φ) = dθ sin(φ) = sin(φ) dθ dw = τ dθ We can integrate this to find: W = τθ Analogue of W = r axis W will be negative if τ and θ have opposite signs! dθ β φ dr = dθ 14 Page 7

8 Work & Power The work done by a torque τ acting through a displacement θ is given by: W = τθ The power provided by a constant torque is therefore given by: P dw d = = τ θ = τω dt dt 15 Work & Kinetic Energy: ecall the Work/Kinetic Energy Theorem: K = W NET This is true in general, and hence applies to rotational motion as well as linear motion. So for an object that rotates about a fixed axis: ( f ωi ) WNET 1 K = I ω = 16 Page 8

9 Example: Disk & String A massless string is wrapped 10 times around a disk of mass M = 40 g and radius = 10 cm. The disk is constrained to rotate without friction about a fixed axis though its center. The string is pulled with a force = 10 N until it has unwound. (Assume the string does not slip, and that the disk is initially not spinning). How fast is the disk spinning after the string has unwound? M 17 Disk & String... The work done is W = τ θ The torque is τ = (since φ = 90 o ) The angular displacement θ is π rad/rev x 10 rev. So W = (.1 m)(10 N)(0π rad) = 6.8 J τ θ M 18 Page 9

10 Disk & String... W NET = W = 6.8 J = K = 1 I ω ecall that I for a disk about its central axis is given by: I = 1 M M So 1 K = M W 1 ω = ω (. J) (. 04kg)(. 1) 4W 468 ω= = M ω = 79.5 rad/s 19 Lecture 3, Act 4 Work & Energy Strings are wrapped around the circumference of two solid disks and pulled with identical forces for the same distance. Disk 1 has a bigger radius, but both have the same moment of inertia. Both disks rotate freely around axes though their centers, and start at rest. Which disk has the biggest angular velocity after the pull? (a) disk 1 (b) disk (c) same ω 1 ω 0 Page 10

11 Lecture 3, Act 4 Solution The work done on both disks is the same! W = d The change in kinetic energy of each will therefore also be the same since W = K. But we know K = 1 I ω ω 1 ω So since I 1 = I ω 1 = ω d 1 Lecture 4, Act 1 otations Two wheels can rotate freely about fixed axles through their centers. The wheels have the same mass, but one has twice the radius of the other. orces 1 and are applied as shown. What is / 1 if the angular acceleration of the wheels is the same? (a) 1 (b) (c) 4 1 Page 11

12 Lecture 4, Act 1 Solution We know but τ= τ = I α and I = m so = m α = mα 1 mα = = m α 1 1 Since = 1 = alling weight & pulley A mass m is hung by a string that is wrapped around a pulley of radius attached to a heavy flywheel. The moment of inertia of the pulley + flywheel is I. The string does not slip on the pulley. Starting at rest, how long does it take for the mass to fall a distance L. α I T m a mg L 4 Page 1

13 alling weight & pulley... or the hanging mass use = ma mg - T = ma or the pulley + flywheel use τ = Iα α I τ = T = Iα ealize that a = α T a = I T Now solve for a using the above equations. a m mg m a = g m + I L 5 alling weight & pulley... Using 1-D kinematics (Lecture ) we can solve for the time required for the weight to fall a distance L: L = 1 at t L = a α T I where m a = g m + I a m mg L 6 Page 13

14 otation around a moving axis. A string is wound around a puck (disk) of mass M and radius. The puck is initially lying at rest on a frictionless horizontal surface. The string is pulled with a force and does not slip as it unwinds. What length of string L has unwound after the puck has moved a distance D? M Top view 7 otation around a moving axis... The CM moves according to = MA The distance moved by the CM is thus A = M D = 1 At = M t The disk will rotate about its CM according to τ = Iα So the angular displacement is α = τ = 1 M 1 θ = αt = M t I = M I = 1 M α M A 8 Page 14

15 otation around a moving axis... So we know both the distance moved by the CM and the angle of rotation about the CM as a function of time: D = M t Divide (b) by (a): (a) θ = M t θ = θ = D D (b) The length of string pulled out is L = θ: D θ L L = D 9 Comments on CM acceleration: We just used τ = Iα for rotation about an axis through the CM even though the CM was accelerating! The CM is not an inertial reference frame! Is this OK?? (After all, we can only use = ma in an inertial reference frame). YES! We can always write τ = Iα for an axis through the CM. This is true even if the CM is accelerating. We will prove this when we discuss angular momentum! α M A 30 Page 15

16 olling An object with mass M, radius, and moment of inertia I rolls without slipping down a plane inclined at an angle θ with respect to horizontal. What is its acceleration? Consider CM motion and rotation about the CM separately when solving this problem (like we did with the last problem)... M I θ 31 olling... Static friction f causes rolling. It is an unknown, so we must solve for it. irst consider the free body diagram of the object and use NET = MA CM : In the x direction Mg sin θ -f= MA Now consider rotation about the CM and use τ = Iα realizing that M τ = f and A = α y f x f A = I f A = I θ Mg 3 Page 16

17 olling... We have two equations: Mgsinθ - f = ma f = I A We can combine these to eliminate f: M sin θ A = g M + I I or a sphere: A M A = g M sin θ M + M 5 5 = gsin θ 7 θ 33 Lecture 4, Act otations Two uniform cylinders are machined out of solid aluminum. One has twice the radius of the other. If both are placed at the top of the same ramp and released, which is moving faster at the bottom? (a) bigger one (b) smaller one (c) same 34 Page 17

18 Lecture 4, Act Solution Consider one of them. Say it has radius, mass M and falls a height H. 1 1 Energy conservation: - U = K MgH = I ω + MV but I = 1 M and ω= V 1 V MgH = M MV H MgH = MV + MV = MV Lecture 4, Act Solution So: MgH = 3 MV gh = 3 V 4 4 V gh = 4 3 So, (c) does not depend on size, as long as the shape is the same!! H 36 Page 18

19 Sliding to olling A bowling ball of mass M and radius is thrown with initial velocity v 0. It is initially not rotating. After sliding with kinetic friction along the lane for a distance D it finally rolls without slipping and has a new velocity v f. The coefficient of kinetic friction between the ball and the lane is µ. What is the final velocity, v f, of the ball? v f = ω ω v 0 f = µmg D 37 Sliding to olling... While sliding, the force of friction will accelerate the ball in the -x direction: = -µmg = Ma so a = -µg The speed of the ball is therefore v = v 0 - µgt (a) riction also provides a torque about the CM of the ball. Using τ = Iα and remembering that I = / 5 M for a solid sphere about an axis through its CM: τ = µ Mg = M 5 α 5µg α = 5µ g ω = ω0 + αt = t (b) x v f = ω ω v 0 f = µmg D 38 Page 19

20 We have two equations: Sliding to olling... 5µg v = v0 µ gt (a) ω = t (b) Using (b) we can solve for t as a function of ω: t = ω 5µ g Plugging this into (a) and using v f = ω (the condition for rolling without slipping): vf = 5 v 7 0 Doesn t depend on µ, M, g!! x v f = ω ω v 0 f = µmg D 39 Lecture 4, Act 3 otations A bowling ball (uniform solid sphere) rolls along the floor without slipping. What is the ratio of its rotational kinetic energy to its translational kinetic energy? 1 1 (a) (b) (c) 5 5 I = ecall that M for a solid sphere about 5 an axis through its CM: 40 Page 0

21 Lecture 4, Act 3 Solution The total kinetic energy is partly due to rotation and partly due to translation (CM motion). K = 1 I ω + 1 MV rotational K translational K 41 Lecture 4, Act 3 Solution K = 1 I ω + 1 MV Since it rolls without slipping: ω= V rotational K Translational K K K OT TANS 1 Iω = 1 MV V M 5 = MV = 5 4 Page 1

22 Atwoods Machine with Massive Pulley: A pair of masses are hung over a massive disk-shaped pulley as shown. ind the acceleration of the blocks. or the hanging masses use = ma -m 1 g + T 1 = -m 1 a -m g + T = m a α M y x or the pulley use τ = Iα = I a T 1 T a = I a 1 T 1 - T = Ma (Since I = 1 M for a disk) m 1 m 1 g a m m g 43 Atwoods Machine with Massive Pulley... We have three equations and three unknowns (T 1, T, a). Solve for a. y -m 1 g + T 1 = -m 1 a (1) -m g + T = m a () α M x T 1 -T = 1 (3) Ma T 1 T a m m a = 1 m + m + M g 1 m 1 m 1 g a m m g 44 Page

PHYSICS 149: Lecture 21

PHYSICS 149: Lecture 21 PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30

More information

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1 Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Rotational Kinematics and Energy Rotational Kinetic Energy, Moment of Inertia All elements inside the rigid

More information

Classical Mechanics Lecture 15

Classical Mechanics Lecture 15 Classical Mechanics Lecture 5 Today s Concepts: a) Parallel Axis Theorem b) Torque & Angular Acceleration Mechanics Lecture 5, Slide Unit 4 Main Points Mechanics Lecture 4, Slide Unit 4 Main Points Mechanics

More information

Physics 131: Lecture 21. Today s Agenda

Physics 131: Lecture 21. Today s Agenda Physics 131: Lecture 1 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 01: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia

More information

Physics 111. Lecture 23 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, Kinetic Energy of Rolling Object

Physics 111. Lecture 23 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, Kinetic Energy of Rolling Object Physics 111 Lecture 3 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, 009 Lecture 3 1/4 Kinetic Energy of Rolling Object Total kinetic energy of a rolling object is the sum of

More information

Physics 131: Lecture 21. Today s Agenda

Physics 131: Lecture 21. Today s Agenda Physics 131: Lecture 21 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia

More information

Name: Date: Period: AP Physics C Rotational Motion HO19

Name: Date: Period: AP Physics C Rotational Motion HO19 1.) A wheel turns with constant acceleration 0.450 rad/s 2. (9-9) Rotational Motion H19 How much time does it take to reach an angular velocity of 8.00 rad/s, starting from rest? Through how many revolutions

More information

= 2 5 MR2. I sphere = MR 2. I hoop = 1 2 MR2. I disk

= 2 5 MR2. I sphere = MR 2. I hoop = 1 2 MR2. I disk A sphere (green), a disk (blue), and a hoop (red0, each with mass M and radius R, all start from rest at the top of an inclined plane and roll to the bottom. Which object reaches the bottom first? (Use

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

Review questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.

Review questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the

More information

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a

More information

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Strike (Day 10) Prelectures, checkpoints, lectures continue with no change. Take-home quizzes this week. See Elaine Schulte s email. HW

More information

16. Rotational Dynamics

16. Rotational Dynamics 6. Rotational Dynamics A Overview In this unit we will address examples that combine both translational and rotational motion. We will find that we will need both Newton s second law and the rotational

More information

Rotation. Kinematics Rigid Bodies Kinetic Energy. Torque Rolling. featuring moments of Inertia

Rotation. Kinematics Rigid Bodies Kinetic Energy. Torque Rolling. featuring moments of Inertia Rotation Kinematics Rigid Bodies Kinetic Energy featuring moments of Inertia Torque Rolling Angular Motion We think about rotation in the same basic way we do about linear motion How far does it go? How

More information

Review. Checkpoint 2 / Lecture 13. Strike (Day 8)

Review. Checkpoint 2 / Lecture 13. Strike (Day 8) Physics 101: Lecture 14 Parallel Axis Theorem, Rotational Energy, Conservation of Energy Examples, and a Little Torque Review Rotational Kinetic Energy K rot = ½ I w 2 Rotational Inertia I = S m i r i2

More information

Rotational Dynamics continued

Rotational Dynamics continued Chapter 9 Rotational Dynamics continued 9.4 Newton s Second Law for Rotational Motion About a Fixed Axis ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS I = ( mr 2

More information

Rotational Kinematics

Rotational Kinematics Rotational Kinematics Rotational Coordinates Ridged objects require six numbers to describe their position and orientation: 3 coordinates 3 axes of rotation Rotational Coordinates Use an angle θ to describe

More information

Rotational Kinematics and Dynamics. UCVTS AIT Physics

Rotational Kinematics and Dynamics. UCVTS AIT Physics Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,

More 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

Lecture 7 Chapter 10,11

Lecture 7 Chapter 10,11 Lecture 7 Chapter 10,11 Rotation, Inertia, Rolling, Torque, and Angular momentum Demo Demos Summary of Concepts to Cover from chapter 10 Rotation Rotating cylinder with string wrapped around it: example

More information

Physics 101 Lecture 12 Equilibrium and Angular Momentum

Physics 101 Lecture 12 Equilibrium and Angular Momentum Physics 101 Lecture 1 Equilibrium and Angular Momentum Ali ÖVGÜN EMU Physics Department www.aovgun.com Static Equilibrium q Equilibrium and static equilibrium q Static equilibrium conditions n Net external

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

Rotational Kinetic Energy

Rotational Kinetic Energy Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body

More information

Rolling without slipping Angular Momentum Conservation of Angular Momentum. Physics 201: Lecture 19, Pg 1

Rolling without slipping Angular Momentum Conservation of Angular Momentum. Physics 201: Lecture 19, Pg 1 Physics 131: Lecture Today s Agenda Rolling without slipping Angular Momentum Conservation o Angular Momentum Physics 01: Lecture 19, Pg 1 Rolling Without Slipping Rolling is a combination o rotation and

More information

Rotation review packet. Name:

Rotation review packet. Name: Rotation review packet. Name:. A pulley of mass m 1 =M and radius R is mounted on frictionless bearings about a fixed axis through O. A block of equal mass m =M, suspended by a cord wrapped around the

More information

Physics 4A Solutions to Chapter 10 Homework

Physics 4A Solutions to Chapter 10 Homework Physics 4A Solutions to Chapter 0 Homework Chapter 0 Questions: 4, 6, 8 Exercises & Problems 6, 3, 6, 4, 45, 5, 5, 7, 8 Answers to Questions: Q 0-4 (a) positive (b) zero (c) negative (d) negative Q 0-6

More information

Assignment 9. to roll without slipping, how large must F be? Ans: F = R d mgsinθ.

Assignment 9. to roll without slipping, how large must F be? Ans: F = R d mgsinθ. Assignment 9 1. A heavy cylindrical container is being rolled up an incline as shown, by applying a force parallel to the incline. The static friction coefficient is µ s. The cylinder has radius R, mass

More information

Angular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion

Angular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion Angular velocity and angular acceleration CHAPTER 9 ROTATION! r i ds i dθ θ i Angular velocity and angular acceleration! equations of rotational motion Torque and Moment of Inertia! Newton s nd Law for

More information

Rolling, Torque & Angular Momentum

Rolling, Torque & Angular Momentum PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the

More information

Name Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass?

Name Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass? NOTE: ignore air resistance in all Questions. In all Questions choose the answer that is the closest!! Question I. (15 pts) Rotation 1. (5 pts) A bowling ball that has an 11 cm radius and a 7.2 kg mass

More information

Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved:

Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved: 8) roller coaster starts with a speed of 8.0 m/s at a point 45 m above the bottom of a dip (see figure). Neglecting friction, what will be the speed of the roller coaster at the top of the next slope,

More information

Lecture 16: Rotational Dynamics

Lecture 16: Rotational Dynamics Lecture 6: otational Dynamics Today s Concepts: a) olling Kine6c Energy b) Angular Accelera6on Mechanics Lecture 6, Slide I felt like every slide just had a ton of equa6ons just being used to find new

More information

PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1

PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1 PHYSICS 220 Lecture 15 Angular Momentum Textbook Sections 9.3 9.6 Lecture 15 Purdue University, Physics 220 1 Last Lecture Overview Torque = Force that causes rotation τ = F r sin θ Work done by torque

More information

Chapter 10: Dynamics of Rotational Motion

Chapter 10: Dynamics of Rotational Motion Chapter 10: Dynamics of Rotational Motion What causes an angular acceleration? The effectiveness of a force at causing a rotation is called torque. QuickCheck 12.5 The four forces shown have the same strength.

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

is acting on a body of mass m = 3.0 kg and changes its velocity from an initial

is acting on a body of mass m = 3.0 kg and changes its velocity from an initial PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block

More information

31 ROTATIONAL KINEMATICS

31 ROTATIONAL KINEMATICS 31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have

More information

ΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω

ΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω Thur Oct 22 Assign 9 Friday Today: Torques Angular Momentum x θ v ω a α F τ m I Roll without slipping: x = r Δθ v LINEAR = r ω a LINEAR = r α ΣF = ma Στ = Iα ½mv 2 ½Iω 2 I POINT = MR 2 I HOOP = MR 2 I

More 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

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

Rotational motion problems

Rotational motion problems Rotational motion problems. (Massive pulley) Masses m and m 2 are connected by a string that runs over a pulley of radius R and moment of inertia I. Find the acceleration of the two masses, as well as

More information

Forces of Rolling. 1) Ifobjectisrollingwith a com =0 (i.e.no netforces), then v com =ωr = constant (smooth roll)

Forces of Rolling. 1) Ifobjectisrollingwith a com =0 (i.e.no netforces), then v com =ωr = constant (smooth roll) Physics 2101 Section 3 March 12 rd : Ch. 10 Announcements: Mid-grades posted in PAW Quiz today I will be at the March APS meeting the week of 15-19 th. Prof. Rich Kurtz will help me. Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101-3/

More information

Lesson 8. Luis Anchordoqui. Physics 168. Thursday, October 11, 18

Lesson 8. Luis Anchordoqui. Physics 168. Thursday, October 11, 18 Lesson 8 Physics 168 1 Rolling 2 Intuitive Question Why is it that when a body is rolling on a plane without slipping the point of contact with the plane does not move? A simple answer to this question

More information

Rotational Motion and Torque

Rotational Motion and Torque Rotational Motion and Torque Introduction to Angular Quantities Sections 8- to 8-2 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is

More information

1301W.600 Lecture 16. November 6, 2017

1301W.600 Lecture 16. November 6, 2017 1301W.600 Lecture 16 November 6, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:30-8:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program

More information

Exam 3 Practice Solutions

Exam 3 Practice Solutions Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

More information

Rotation. Rotational Variables

Rotation. Rotational Variables Rotation Rigid Bodies Rotation variables Constant angular acceleration Rotational KE Rotational Inertia Rotational Variables Rotation of a rigid body About a fixed rotation axis. Rigid Body an object that

More information

Physics 101: Lecture 13 Rotational Kinetic Energy and Rotational Inertia. Physics 101: Lecture 13, Pg 1

Physics 101: Lecture 13 Rotational Kinetic Energy and Rotational Inertia. Physics 101: Lecture 13, Pg 1 Physics 0: Lecture 3 Rotational Kinetic Energy and Rotational Inertia Physics 0: Lecture 3, Pg Overview of Semester Newton s Laws F Net = m a Work-Energy F Net = m a W Net = DKE multiply both sides by

More information

Webreview Torque and Rotation Practice Test

Webreview Torque and Rotation Practice Test Please do not write on test. ID A Webreview - 8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30-m-radius automobile

More information

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is

More 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

Name (please print): UW ID# score last first

Name (please print): UW ID# score last first Name (please print): UW ID# score last first Question I. (20 pts) Projectile motion A ball of mass 0.3 kg is thrown at an angle of 30 o above the horizontal. Ignore air resistance. It hits the ground 100

More information

Rotation and Angles. By torque and energy

Rotation and Angles. By torque and energy Rotation and Angles By torque and energy CPR An experiment - and things always go wrong when you try experiments the first time. (I won t tell you the horror stories of when I first used clickers, Wattle

More information

Translational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work

Translational 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 information

Moment of Inertia & Newton s Laws for Translation & Rotation

Moment of Inertia & Newton s Laws for Translation & Rotation Moment of Inertia & Newton s Laws for Translation & Rotation In this training set, you will apply Newton s 2 nd Law for rotational motion: Στ = Σr i F i = Iα I is the moment of inertia of an object: I

More information

Physics 8 Wednesday, October 30, 2013

Physics 8 Wednesday, October 30, 2013 Physics 8 Wednesday, October 30, 2013 HW9 (due Friday) is 7 conceptual + 8 calculation problems. Of the 8 calculation problems, 4 or 5 are from Chapter 11, and 3 or 4 are from Chapter 12. 7pm HW sessions:

More information

Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy

Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468 Announcements This

More information

Phys 106 Practice Problems Common Quiz 1 Spring 2003

Phys 106 Practice Problems Common Quiz 1 Spring 2003 Phys 106 Practice Problems Common Quiz 1 Spring 2003 1. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed

More information

Rotation Atwood Machine with Massive Pulley Energy of Rotation

Rotation Atwood Machine with Massive Pulley Energy of Rotation Rotation Atwood Machine with Massive Pulley Energy of Rotation Lana Sheridan De Anza College Nov 21, 2017 Last time calculating moments of inertia the parallel axis theorem Overview applications of moments

More information

Chap10. Rotation of a Rigid Object about a Fixed Axis

Chap10. Rotation of a Rigid Object about a Fixed Axis Chap10. Rotation of a Rigid Object about a Fixed Axis Level : AP Physics Teacher : Kim 10.1 Angular Displacement, Velocity, and Acceleration - A rigid object rotating about a fixed axis through O perpendicular

More information

Chapter 10. Rotation of a Rigid Object about a Fixed Axis

Chapter 10. Rotation of a Rigid Object about a Fixed Axis Chapter 10 Rotation of a Rigid Object about a Fixed Axis Angular Position Axis of rotation is the center of the disc Choose a fixed reference line. Point P is at a fixed distance r from the origin. A small

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

Torque/Rotational Energy Mock Exam. Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK.

Torque/Rotational Energy Mock Exam. Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK. AP Physics C Spring, 2017 Torque/Rotational Energy Mock Exam Name: Answer Key Mr. Leonard Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK. (22 pts ) 1. Two masses are attached

More information

Torque. Introduction. Torque. PHY torque - J. Hedberg

Torque. Introduction. Torque. PHY torque - J. Hedberg Torque PHY 207 - torque - J. Hedberg - 2017 1. Introduction 2. Torque 1. Lever arm changes 3. Net Torques 4. Moment of Rotational Inertia 1. Moment of Inertia for Arbitrary Shapes 2. Parallel Axis Theorem

More information

Physics 5A Final Review Solutions

Physics 5A Final Review Solutions Physics A Final Review Solutions Eric Reichwein Department of Physics University of California, Santa Cruz November 6, 0. A stone is dropped into the water from a tower 44.m above the ground. Another stone

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

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

Rotational Motion. Rotational Motion. Rotational Motion

Rotational Motion. Rotational Motion. Rotational Motion I. Rotational Kinematics II. Rotational Dynamics (Netwton s Law for Rotation) III. Angular Momentum Conservation 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x =

More information

Chapters 10 & 11: Rotational Dynamics Thursday March 8 th

Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Review of rotational kinematics equations Review and more on rotational inertia Rolling motion as rotation and translation Rotational kinetic energy

More information

Work and kinetic Energy

Work and kinetic Energy Work and kinetic Energy Problem 66. M=4.5kg r = 0.05m I = 0.003kgm 2 Q: What is the velocity of mass m after it dropped a distance h? (No friction) h m=0.6kg mg Work and kinetic Energy Problem 66. M=4.5kg

More information

Phys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1

Phys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Q1. A water molecule (H 2O) consists of an oxygen (O) atom of mass 16m and two hydrogen (H) atoms, each of mass m, bound to it (see Figure

More information

AP Physics. Harmonic Motion. Multiple Choice. Test E

AP Physics. Harmonic Motion. Multiple Choice. Test E AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.

More information

Rolling, Torque, and Angular Momentum

Rolling, Torque, and Angular Momentum AP Physics C Rolling, Torque, and Angular Momentum Introduction: Rolling: In the last unit we studied the rotation of a rigid body about a fixed axis. We will now extend our study to include cases where

More information

1 MR SAMPLE EXAM 3 FALL 2013

1 MR SAMPLE EXAM 3 FALL 2013 SAMPLE EXAM 3 FALL 013 1. A merry-go-round rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,

More information

= y(x, t) =A cos (!t + kx)

= y(x, t) =A cos (!t + kx) A harmonic wave propagates horizontally along a taut string of length L = 8.0 m and mass M = 0.23 kg. The vertical displacement of the string along its length is given by y(x, t) = 0. m cos(.5 t + 0.8

More information

Rotation Work and Power of Rotation Rolling Motion Examples and Review

Rotation Work and Power of Rotation Rolling Motion Examples and Review Rotation Work and Power of Rotation Rolling Motion Examples and Review Lana Sheridan De Anza College Nov 22, 2017 Last time applications of moments of inertia Atwood machine with massive pulley kinetic

More information

Angular Displacement. θ i. 1rev = 360 = 2π rads. = "angular displacement" Δθ = θ f. π = circumference. diameter

Angular Displacement. θ i. 1rev = 360 = 2π rads. = angular displacement Δθ = θ f. π = circumference. diameter Rotational Motion Angular Displacement π = circumference diameter π = circumference 2 radius circumference = 2πr Arc length s = rθ, (where θ in radians) θ 1rev = 360 = 2π rads Δθ = θ f θ i = "angular displacement"

More information

Chapter 8- Rotational Kinematics Angular Variables Kinematic Equations

Chapter 8- Rotational Kinematics Angular Variables Kinematic Equations Chapter 8- Rotational Kinematics Angular Variables Kinematic Equations Chapter 9- Rotational Dynamics Torque Center of Gravity Newton s 2 nd Law- Angular Rotational Work & Energy Angular Momentum Angular

More information

Chapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics

Chapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I

More information

AP Physics 1- Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law- F = Ma cm. Usually the location of the center

More information

Physics 2210 Homework 18 Spring 2015

Physics 2210 Homework 18 Spring 2015 Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle

More information

Your Name: PHYSICS 101 MIDTERM. Please circle your section 1 9 am Galbiati 2 10 am Kwon 3 11 am McDonald 4 12:30 pm McDonald 5 12:30 pm Kwon

Your Name: PHYSICS 101 MIDTERM. Please circle your section 1 9 am Galbiati 2 10 am Kwon 3 11 am McDonald 4 12:30 pm McDonald 5 12:30 pm Kwon 1 Your Name: PHYSICS 101 MIDTERM October 26, 2006 2 hours Please circle your section 1 9 am Galbiati 2 10 am Kwon 3 11 am McDonald 4 12:30 pm McDonald 5 12:30 pm Kwon Problem Score 1 /13 2 /20 3 /20 4

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

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

Suggested Problems. Chapter 1

Suggested Problems. Chapter 1 Suggested Problems Ch1: 49, 51, 86, 89, 93, 95, 96, 102. Ch2: 9, 18, 20, 44, 51, 74, 75, 93. Ch3: 4, 14, 46, 54, 56, 75, 91, 80, 82, 83. Ch4: 15, 59, 60, 62. Ch5: 14, 52, 54, 65, 67, 83, 87, 88, 91, 93,

More 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

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

Lecture 6 Physics 106 Spring 2006

Lecture 6 Physics 106 Spring 2006 Lecture 6 Physics 106 Spring 2006 Angular Momentum Rolling Angular Momentum: Definition: Angular Momentum for rotation System of particles: Torque: l = r m v sinφ l = I ω [kg m 2 /s] http://web.njit.edu/~sirenko/

More information

Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1

Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 1. A 50-kg boy and a 40-kg girl sit on opposite ends of a 3-meter see-saw. How far from the girl should the fulcrum be placed in order for the

More information

AP Physics 1 Rotational Motion Practice Test

AP Physics 1 Rotational Motion Practice Test AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able

More information

University Physics (Prof. David Flory) Chapt_11 Thursday, November 15, 2007 Page 1

University Physics (Prof. David Flory) Chapt_11 Thursday, November 15, 2007 Page 1 University Physics (Prof. David Flory) Chapt_11 Thursday, November 15, 2007 Page 1 Name: Date: 1. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on

More information

Chapter 8 Rotational Motion and Equilibrium

Chapter 8 Rotational Motion and Equilibrium Chapter 8 Rotational Motion and Equilibrium 8.1 Rigid Bodies, Translations, and Rotations A rigid body is an object or a system of particles in which the distances between particles are fixed (remain constant).

More information

Phys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw

Phys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the

More information

Physics 2210 Fall smartphysics 16 Rotational Dynamics 11/13/2015

Physics 2210 Fall smartphysics 16 Rotational Dynamics 11/13/2015 Physics 10 Fall 015 smartphysics 16 Rotational Dynamics 11/13/015 A rotor consists of a thin rod of length l=60 cm, mass m=10.0 kg, with two spheres attached to the ends. Each sphere has radius R=10 cm,

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

Centripetal acceleration ac = to2r Kinetic energy of rotation KE, = \lto2. Moment of inertia. / = mr2 Newton's second law for rotational motion t = la

Centripetal acceleration ac = to2r Kinetic energy of rotation KE, = \lto2. Moment of inertia. / = mr2 Newton's second law for rotational motion t = la The Language of Physics Angular displacement The angle that a body rotates through while in rotational motion (p. 241). Angular velocity The change in the angular displacement of a rotating body about

More information

A) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2.

A) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2. Coordinator: Dr. W. Al-Basheer Thursday, July 30, 2015 Page: 1 Q1. A constant force F ( 7.0ˆ i 2.0 ˆj ) N acts on a 2.0 kg block, initially at rest, on a frictionless horizontal surface. If the force causes

More information

Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow)

Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Name (printed) Lab Section(+2 pts) Name (signed as on ID) Multiple choice Section. Circle the correct answer. No work need be shown and no partial

More information

CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY

CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY OUTLINE 1. Angular Position, Velocity, and Acceleration 2. Rotational

More information

A Ferris wheel in Japan has a radius of 50m and a mass of 1.2 x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at

A Ferris wheel in Japan has a radius of 50m and a mass of 1.2 x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at Option B Quiz 1. A Ferris wheel in Japan has a radius of 50m and a mass of 1. x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at rest, what is the wheel s angular acceleration?

More information