# 1. A radian is about: A. 25 ± B. 37 ± C. 45 ± D. 57 ± E. 90 ± ans: D Section: 10{2; Di±culty: E

Save this PDF as:

Size: px
Start display at page:

Download "1. A radian is about: A. 25 ± B. 37 ± C. 45 ± D. 57 ± E. 90 ± ans: D Section: 10{2; Di±culty: E"

## Transcription

2 6 The angular speed of the second hand of a watch is: A (¼=1800) rad=s B (¼=60) m=s C (¼=30) m=s D (2¼)m=s E (60) m=s Section: 10{2; Di±culty: E 7 The angular speed of the minute hand of a watch is: A (60=¼)m=s B (1800=¼)m=s C (¼)m=s D (¼=1800) m=s E (¼=60) m=s Section: 10{2; Di±culty: E 8 Ten seconds after an electric fan is turned on, the fan rotates at 300 rev=min Its average angular acceleration is: A 3:14 rad=s 2 B 30 rad=s 2 C 30 rev=s 2 D 50 rev=min 2 E 1800 rev=s 2 Section: 10{2; Di±culty: E 9 A ywheel rotating at 12 rev=s is brought to rest in 6 s The magnitude of the average angular acceleration in rad/s 2 of the wheel during this process is: A 1=¼ B 2 C 4 D 4¼ E 72 Section: 10{2; Di±culty: E 160 Chapter 10: ROTATION

7 ²²²²² 26 A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m The total angle through which she revolves is: A 50 rad B 75 rad C 150 rad D 314 rad E none of these Section: 10{5; Di±culty: E 27 The gure shows a cylinder of radius 0:7m rotating about its axis at 10rad=s The speed of the point P is: P ² ² A 7:0m=s B 14¼ rad=s C 7:0¼ rad=s D 0:70 m=s E none of these Section: 10{5; Di±culty: E 28 The fan shown has been turned on and is now slowing as it rotates clockwise The direction of the acceleration of the point X on the fan tip could be: ² X A B & C # D Ã E! Section: 10{5; Di±culty: E Chapter 10: ROTATION 165

8 29 A wheel of diameter 3:0cmhasa4:0-m cord wrapped around its periphery Starting from rest, the wheel is given a constant angular acceleration of 2:0rad=s 2 The cord will unwind in: A 0:82 s B 2:0s C 8:0s D 16 s E 130 s Section: 10{5; Di±culty: M 30 A particle moves in a circular path of radius 0:10 m with a constant angular speed of 5 rev=s The acceleration of the particle is: A 0:10¼ m=s 2 B 0:50 m=s 2 C 500¼ m=s 2 D 1000¼ 2 m=s 2 E 10¼ 2 m=s 2 Section: 10{5; Di±culty: E 31 A car travels north at constant velocity It goes over a piece of mud, which sticks to the tire The initial acceleration of the mud, as it leaves the ground, is: A vertically upward B horizontally to the north C horizontally to the south D zero E upward and forward at 45 ± to the horizontal Section: 10{5; Di±culty: E 32 Wrapping paper is being from a 5:0-cm radius tube, free to rotate on its axis If it is pulled at the constant rate of 10 cm=s and does not slip on the tube, the angular velocity of the tube is: A 2:0rad=s B 5:0rad=s C 10 rad=s D 25 rad=s E 50 rad=s Section: 10{5; Di±culty: E 166 Chapter 10: ROTATION

9 33 String is wrapped around the periphery of a 5:0-cm radius cylinder, free to rotate on its axis The string is pulled straight out at a constant rate of 10 cm=s and does not slip on the cylinder As each small segment of string leaves the cylinder, its acceleration changes by: A 0 B 0:010 m=s 2 C 0:020 m=s 2 D 0:10 m=s 2 E 0:20 m=s 2 Section: 10{5; Di±culty: M 34 A ywheel of diameter 1:2 m has a constant angular acceleration of 5:0rad=s 2 The tangential acceleration of a point on its rim is: A 5:0rad=s 2 B 3:0m=s 2 C 5:0m=s 2 D 6:0m=s 2 E 12 m=s 2 Section: 10{5; Di±culty: E 35 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 of a point halfway between the center and the rim is: A 1 B 2 C 1=2 D 4 E 1=4 Section: 10{5; Di±culty: E 36 For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is: A 1 B 2 C 1=2 D 4 E 1=4 Section: 10{5; Di±culty: E Chapter 10: ROTATION 167

10 37 For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is: A 1 B 2 C 1=2 D 4 E 1=4 Section: 10{5; Di±culty: E 38 Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is: A 1 B 2 C 1=2 D 4 E 1=4 Section: 10{5; Di±culty: E 39 The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if: A the magnitudes of the angular velocity and the angular acceleration are each multiplied by afactorof4 B the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed C the magnitudes of the angular velocity and the angular acceleration are each multiplied by afactorof2 D the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed E the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4 Section: 10{5; Di±culty: M 40 If a wheel turns with constant angular speed then: A each point on its rim moves with constant velocity B each point on its rim moves with constant acceleration C the wheel turns through equal angles in equal times D the angle through which the wheel turns in each second increases as time goes on E the angle through which the wheel turns in each second decreases as time goes on Section: 10{2, 5; Di±culty: E 168 Chapter 10: ROTATION

11 41 A wheel starts from rest and spins with a constant angular acceleration As time goes on the acceleration vector for a point on the rim: A decreases in magnitude and becomes more nearly tangent to the rim B decreases in magnitude and becomes more early radial C increases in magnitude and becomes more nearly tangent to the rim D increases in magnitude and becomes more nearly radial E increases in magnitude but retains the same angle with the tangent to the rim Section: 10{4, 5; Di±culty: M 42 A pulley with a radius of 3:0 cm and a rotational inertia of 4: kg m 2 is suspended from the ceiling A rope passes over it with a 2:0-kg block attached to one end and a 4:0-kg block attached to the other The rope does not slip on the pulley When the speed of the heavier block is 2:0m=s the kinetic energy of the pulley is: A 0:15 J B 0:30 J C 1:0J D 10 J E 20 J Section: 10{5, 6; Di±culty: M 43 A pulley with a radius of 3:0 cm and a rotational inertia of 4: kg m 2 is suspended from the ceiling A rope passes over it with a 2:0-kg block attached to one end and a 4:0-kg block attached to the other The rope does not slip on the pulley At any instant after the blocks start moving, the object with the greatest kinetic energy is: A the heavier block B the lighter block C the pulley D either block (the two blocks have the same kinetic energy) E none (all three objects have the same kinetic energy) Section: 10{5, 6; Di±culty: M Chapter 10: ROTATION 169

12 ²²²²² ²²²²² 44 Three identical balls are tied by light strings to the same rod and rotate around it, as shown below Rank the balls according to their rotational inertia, least to greatest 1m ² ²² ball 1 2m ²²² ball 2 3m ²²² ball 3 A 1, 2, 3 B 3, 2, 1 C 3, then 1 and 2 tie D 1, 3, 2 E All are the same 45 Four identical particles, each with mass m, are arranged in the x; y plane as shown They are connected by light sticks to form a rigid body If m =2:0kg and a =1:0 m, the rotational inertia of this array about the y axis is: y a a a ²²²²² ²²²²² x a A 4:0kg m 2 B 12 kg m 2 C 9:6kg m 2 D 4:8kg m 2 E none of these 170 Chapter 10: ROTATION

13 46 Three identical balls, with masses of M, 2M, and3m, are fastened to a massless rod of length L as shown The rotational inertia about the left end of the rod is: Ã L=2!Ã L=2! 3M 2M M ²²²²² ²²²²² ²²²²² A ML 2 =2 B ML 2 C 3ML 2 =2 D 6ML 2 E 3ML 2 =4 47 The rotational inertia of a thin cylindrical shell of mass M, radiusr, and length L about its central axis (X{X 0 )is: A MR 2 =2 B ML 2 =2 C ML 2 D MR 2 E none of these X ² "j X 0 R j# Ã L! 48 The rotational inertia of a wheel about its axle does not depend upon its: A diameter B mass C distribution of mass D speed of rotation E material composition Chapter 10: ROTATION 171

14 49 Consider four objects, each having the same mass and the same radius: 1 a solid sphere 2 a hollow sphere 3 a at disk in the x; y plane 4 ahoopinthex; y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is: A 1, 2, 3, 4 B 4, 3, 2, 1 C 1, 3, 2, 4 D 4, 2, 3, 1 E 3, 1, 2, 4 50 A and B are two solid cylinders made of aluminum Their dimensions are shown The ratio of the rotational inertia of B to that of A about the common axis X{X 0 is: R " # A X X 0 B " j 2R j # A 2 B 4 C 8 D 16 E 32 Section: 10{7; Di±culty: M Ã L! Ã 2L! 51 Two uniform circular disks having the same mass and the same thickness are made from di erent materials The disk with the smaller rotational inertia is: A the one made from the more dense material B the one made from the less dense material C neither both rotational inertias are the same D the disk with the larger angular velocity E the disk with the larger torque 172 Chapter 10: ROTATION

16 56 The rotational inertia of a solid uniform sphere about a diameter is (2=5)MR 2,whereM is its mass and R isitsradius Ifthesphereispivotedaboutanaxisthatistangenttoitssurface, its rotational inertia is: A MR 2 B (2=5)MR 2 C (3=5)MR 2 D (5=2)MR 2 E (7=5)MR 2 57 A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2=5)MR 2 A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling Its rotational inertia about the point of attachment at the ceiling is: A (2=5)MR 2 B 9MR 2 C 16MR 2 D (47=5)MR 2 E (82=5)MR 2 58 A force with a given magnitude is to be applied to a wheel The torque can be maximized by: A applying the force near the axle, radially outward from the axle B applying the force near the rim, radially outward from the axle C applying the force near the axle, parallel to a tangent to the wheel D applying the force at the rim, tangent to the rim E applying the force at the rim, at 45 ± to the tangent Section: 10{8; Di±culty: E 174 Chapter 10: ROTATION

17 59 The meter stick shown below rotates about an axis through the point marked ², 20 cm from one end Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown The magnitudes of the forces are all the same Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest ~F 1 ~F 3 0cm ² 20 cm ~F 2 ~F 4 40 cm 60 cm 80 cm 100 cm ~F 5 A F1 ~, F ~ 2, F ~ 3, F ~ 4, F ~ 5 B F1 ~ and F ~ 2 tie, then F ~ 3, F ~ 4, F ~ 5 C F2 ~ and F ~ 5 tie, then F ~ 4, F ~ 1, F ~ 3 D F2 ~, F ~ 5, F ~ 1 and F ~ 3 tie, then F ~ 4 E F2 ~ and F ~ 5 tie, then F ~ 4,then F ~ 1 and F ~ 3 tie Section: 10{8; Di±culty: E 60 A rod is pivoted about its center A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown The magnitude of the total torque about the pivot (in N m) is: 5N 30 ± ² 2:0m 4:0m 30 ± A 0 B 5 C 8:7 D 15 E 26 Section: 10{8; Di±culty: M 5N Chapter 10: ROTATION 175

18 61 A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark It is initially at rest A horizontal force ~ F 1 is applied perpendicularly to the end of the stick at 0 cm, as shown A second horizontal force ~ F 2 (not shown) is applied at the 100-cm end of the stick If the stick does not rotate: ~F 1 0cm ² 20 cm 40 cm 60 cm 80 cm 100 cm A j F ~ 2 j > j F ~ 1 j for all orientations of F ~ 2 B j F ~ 2 j < j F ~ 1 j for all orientations of F ~ 2 C j F ~ 2 j = j F ~ 1 j for all orientations of F ~ 2 D j F ~ 2 j > j F ~ 1 j for some orientations of F ~ 2 and j F ~ 2 j < j F ~ 1 j for others E j F ~ 2 j > j F ~ 1 j for some orientations of F ~ 2 and j F ~ 2 j = j F ~ 1 j for others Section: 10{8; Di±culty: E 62 = I for an object rotating about a xed axis, where is the net torque acting on it, I is its rotational inertia, and is its angular acceleration This expression: A is the de nition of torque B is the de nition of rotational inertia C is the de nition of angular acceleration D follows directly from Newton's second law E depends on a principle of physics that is unrelated to Newton's second law Section: 10{9; Di±culty: E 63 A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a xed axis through its center Assume the hoop is connected to the rotation axis by light spokes With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown Rank the objects according to their angular accelerations, least to greatest disk hoop sphere ² ² ² ² ~F ~F ~F A disk, hoop, sphere B hoop, disk, sphere C hoop, sphere, disk D hoop, disk, sphere E sphere, disk, hoop Section: 10{7, 8, 9; Di±culty: E 176 Chapter 10: ROTATION

21 72 A 16-kg block is attached to a cord that is wrapped around the rim of a ywheel of diameter 0:40 m and hangs vertically, as shown The rotational inertia of the ywheel is 0:50 kg m 2 When the block is released and the cord unwinds, the acceleration of the block is: " jj 0:4m j # ² 16 kg A 0:15g B 0:56g C 0:84g D g E 1:3g Section: 10{4, 5, 9; Di±culty: M 73 A 0:70-kg disk with a rotational inertia given by MR 2 =2isfreetorotateona xedhorizontal axis suspended from the ceiling A string is wrapped around the disk and a 2:0-kg mass hangs from the free end If the string does not slip, then as the mass falls and the cylinder rotates, the suspension holding the cylinder pulls up on the cylinder with a force of: A 6:9N B 9:8N C 16 N D 26 N E 29 N Section: 10{4, 5, 9; Di±culty: M Chapter 10: ROTATION 179

22 74 A small disk of radius R 1 is mounted coaxially with a larger disk of radius R 2 The disks aresecurelyfastenedtoeachotherandthecombinationisfreetorotateona xedaxlethat is perpendicular to a horizontal frictionless table top, as shown in the overhead view below The rotational inertia of the combination is I A string is wrapped around the larger disk and attached to a block of mass m, on the table Another string is wrapped around the smaller diskandispulledwithaforce ~ F as shown The acceleration of the block is: R 2 m ² R 1 ~F A R 1 F=mR 2 B R 1 R 2 F=(I 2) C R 1 R 2 F=(I + mr2) 2 D R 1 R 2 F=(I mr 1 R 2 ) E R 1 R 2 F=(I + mr 1 R 2 ) Section: 10{5, 8, 9; Di±culty: M 75 A small disk of radius R 1 is fastened coaxially to a larger disk of radius R 2 The combination is free to rotate on a xed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below The rotational inertia of the combination is I Astring iswrappedaroundthelargerdiskandattachedtoablockofmassm, on the table Another string is wrapped around the smaller disk and is pulled with a force ~ F as shown The tension in the string pulling the block is: R 2 m ² R 1 ~F A R 1 F=R 2 B mr 1 R 2 F=(I mr 2 2) C mr 1 R 2 F=(I + mr 2 2) D mr 1 R 2 F=(I mr 1 R 2 ) E mr 1 R 2 F=(I + mr 1 R 2 ) Section: 10{5, 8, 9; Di±culty: M 180 Chapter 10: ROTATION

23 76 A block is attached to each end of a rope that passes over a pulley suspended from the ceiling Theblocksdonothavethesamemass Iftheropedoesnotsliponthepulley,thenatany instant after the blocks start moving, the rope: A pullsonbothblocks,butexertsagreaterforceontheheavierblock B pulls on both blocks, but exerts a greater force on the lighter block C pullsonbothblocksandexertsthesamemagnitudeforceonbothblocks D does not pull on either block E pulls only on the lighter block Section: 10{8, 9; Di±culty: E 77 A disk with a rotational inertia of 5:0kg m 2 and a radius of 0:25 m rotates on a xed axis perpendicular to the disk and through its center A force of 2:0 N is applied tangentially to the rim As the disk turns through half a revolution the work done by the force is: A 1:6J B 2:5J C 6:3J D 10 J E 40 J Section: 10{10; Di±culty: E 78 A circular saw is powered by a motor When the saw is used to cut wood, the wood exerts a torque of 0:80 N m on the saw blade If the blade rotates with a constant angular velocity of 20 rad=s the work done on the blade by the motor in 1:0 min is: A 0 B 480 J C 960 J D 1400 J E 1800 J Section: 10{10; Di±culty: E 79 A disk has a rotational inertia of 6:0kg m 2 and a constant angular acceleration of 2:0rad=s 2 If it starts from rest the work done during the rst 5:0 s by the net torque acting on it is: A 0 B 30 J C 60 J D 300 J E 600 J Section: 10{4, 6, 10; Di±culty: M Chapter 10: ROTATION 181

24 80 A disk starts from rest and rotates around a xed axis, subject to a constant net torque The work done by the torque during the second 5 s is as the work done during the rst 5 s A the same B twice as much C half as much D fourtimesasmuch E one-fourth as much Section: 10{4, 6, 10; Di±culty: M 81 A disk starts from rest and rotates about a xed axis, subject to a constant net torque The work done by the torque during the second revolution is as the work done during the rst revolution A the same B twice as much C half as much D fourtimesasmuch E one-fourth as much Section: 10{4, 6, 10; Di±culty: M 182 Chapter 10: ROTATION

### PHYSICS 111 HOMEWORK SOLUTION #10. April 10, 2013

PHYSICS 111 HOMEWORK SOLUTION #10 April 10, 013 0.1 Given M = 4 i + j 3 k and N = i j 5 k, calculate the vector product M N. By simply following the rules of the cross product: i i = j j = k k = 0 i j

### Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

### PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be

### Unit 4 Practice Test: Rotational Motion

Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle

### 11. Rotation Translational Motion: Rotational Motion:

11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational

### PHYS 211 FINAL FALL 2004 Form A

1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each

### Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.

Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems

### 226 Chapter 15: OSCILLATIONS

Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion

### Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

### Rotation. Moment of inertia of a rotating body: w I = r 2 dm

Rotation Moment of inertia of a rotating body: w I = r 2 dm Usually reasonably easy to calculate when Body has symmetries Rotation axis goes through Center of mass Exams: All moment of inertia will be

### PHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?

1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always

### Lab 7: Rotational Motion

Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

### HW Set VI page 1 of 9 PHYSICS 1401 (1) homework solutions

HW Set VI page 1 of 9 10-30 A 10 g bullet moving directly upward at 1000 m/s strikes and passes through the center of mass of a 5.0 kg block initially at rest (Fig. 10-33 ). The bullet emerges from the

Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### PHY121 #8 Midterm I 3.06.2013

PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

### 3600 s 1 h. 24 h 1 day. 1 day

Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### PHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013

PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.

### PHY231 Section 1, Form B March 22, 2012

1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate

### Chapter 8: Rotational Motion of Solid Objects

Chapter 8: Rotational Motion of Solid Objects 1. An isolated object is initially spinning at a constant speed. Then, although no external forces act upon it, its rotational speed increases. This must be

### Linear Motion vs. Rotational Motion

Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a

### 1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true?

Physics 2A, Sec C00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to ll your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

### PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in

### 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

### Chapter 3.8 & 6 Solutions

Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled

### Solution Derivations for Capa #11

Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform

### Chapter 4 Dynamics: Newton s Laws of Motion

Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the NormalForce

### Exam 3 Review Questions PHY Exam 3

Exam 3 Review Questions PHY 2425 - Exam 3 Section: 8 1 Topic: Conservation of Linear Momentum Type: Numerical 1 An automobile of mass 1300 kg has an initial velocity of 7.20 m/s toward the north and a

### Rotational inertia (moment of inertia)

Rotational inertia (moment of inertia) Define rotational inertia (moment of inertia) to be I = Σ m i r i 2 or r i : the perpendicular distance between m i and the given rotation axis m 1 m 2 x 1 x 2 Moment

### Physics 201 Homework 8

Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the

### Angular acceleration α

Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

### Lecture 16. Newton s Second Law for Rotation. Moment of Inertia. Angular momentum. Cutnell+Johnson: 9.4, 9.6

Lecture 16 Newton s Second Law for Rotation Moment of Inertia Angular momentum Cutnell+Johnson: 9.4, 9.6 Newton s Second Law for Rotation Newton s second law says how a net force causes an acceleration.

### C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

### Physics 1401 - Exam 2 Chapter 5N-New

Physics 1401 - Exam 2 Chapter 5N-New 2. The second hand on a watch has a length of 4.50 mm and makes one revolution in 60.00 s. What is the speed of the end of the second hand as it moves in uniform circular

### 5.2 Rotational Kinematics, Moment of Inertia

5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position

### Center of Gravity. We touched on this briefly in chapter 7! x 2

Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.

### Physics 1653 Exam 3 - Review Questions

Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

### Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

### Practice Exam Three Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,

### Tennessee State University

Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

### Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.

### Rotational Inertia Demonstrator

WWW.ARBORSCI.COM Rotational Inertia Demonstrator P3-3545 BACKGROUND: The Rotational Inertia Demonstrator provides an engaging way to investigate many of the principles of angular motion and is intended

Answer, Key { Homework 6 { Rubin H Landau 1 This print-out should have 24 questions. Check that it is complete before leaving the printer. Also, multiple-choice questions may continue on the next column

### No Brain Too Small PHYSICS. 2 kg

MECHANICS: ANGULAR MECHANICS QUESTIONS ROTATIONAL MOTION (2014;1) Universal gravitational constant = 6.67 10 11 N m 2 kg 2 (a) The radius of the Sun is 6.96 10 8 m. The equator of the Sun rotates at a

### AP Physics - Chapter 8 Practice Test

AP Physics - Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on

### AP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s

AP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s Answer the multiple choice questions (2 Points Each) on this sheet with capital

### Torque and Rotary Motion

Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straight-forward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,

### VELOCITY, ACCELERATION, FORCE

VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

### AP Physics: Rotational Dynamics 2

Name: Assignment Due Date: March 30, 2012 AP Physics: Rotational Dynamics 2 Problem A solid cylinder with mass M, radius R, and rotational inertia 1 2 MR2 rolls without slipping down the inclined plane

### Physics 1A Lecture 10C

Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium

### Chapter 4 Dynamics: Newton s Laws of Motion

Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal

### B) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B

Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time

### F N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26

Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,

### Centripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.

Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.

### Acceleration due to Gravity

Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision

### TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 3 Section 1 Version 1 December 6, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting.

### CHAPTER 15 FORCE, MASS AND ACCELERATION

CHAPTER 5 FORCE, MASS AND ACCELERATION EXERCISE 83, Page 9. A car initially at rest accelerates uniformly to a speed of 55 km/h in 4 s. Determine the accelerating force required if the mass of the car

### 8.012 Physics I: Classical Mechanics Fall 2008

MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE

### Chapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.

Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal

### circular motion & gravitation physics 111N

circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would

### Physics 41 HW Set 1 Chapter 15

Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,

### Physics 126 Practice Exam #3 Professor Siegel

Physics 126 Practice Exam #3 Professor Siegel Name: Lab Day: 1. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? A) The magnetic force

### Rotational Motion: Moment of Inertia

Experiment 8 Rotational Motion: Moment of Inertia 8.1 Objectives Familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body

### Chapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.

Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed

### SOLID MECHANICS DYNAMICS TUTORIAL MOMENT OF INERTIA. This work covers elements of the following syllabi.

SOLID MECHANICS DYNAMICS TUTOIAL MOMENT OF INETIA This work covers elements of the following syllabi. Parts of the Engineering Council Graduate Diploma Exam D5 Dynamics of Mechanical Systems Parts of the

### Homework 4. problems: 5.61, 5.67, 6.63, 13.21

Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find

### AP Physics Newton's Laws Practice Test

AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a

### This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.

This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical

### Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel

Physics 125 Practice Exam #3 Chapters 6-7 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the

### Chapter 24 Physical Pendulum

Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...

### Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:

Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.

### Work, rotational kinetic energy, torque, disk

264 CHPTER 10 RTTIN Sample Problem Work, rotational kinetic energy, torque, disk et the disk in Fig. 10-18 start from rest at time t 0 and also let the tension in the massless cord be 6.0 N and the angular

### www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity

### Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law

### Curso2012-2013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.

1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.

### CHAPTER 28 THE CIRCLE AND ITS PROPERTIES

CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page 77 1. Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle

### SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS

SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering

### Fall 12 PHY 122 Homework Solutions #8

Fall 12 PHY 122 Homework Solutions #8 Chapter 27 Problem 22 An electron moves with velocity v= (7.0i - 6.0j)10 4 m/s in a magnetic field B= (-0.80i + 0.60j)T. Determine the magnitude and direction of the

### A ball, attached to a cord of length 1.20 m, is set in motion so that it is swinging backwards and forwards like a pendulum.

MECHANICS: SIMPLE HARMONIC MOTION QUESTIONS THE PENDULUM (2014;2) A pendulum is set up, as shown in the diagram. The length of the cord attached to the bob is 1.55 m. The bob has a mass of 1.80 kg. The

### Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is

Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of

### Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

### Fundamental Mechanics: Supplementary Exercises

Phys 131 Fall 2015 Fundamental Mechanics: Supplementary Exercises 1 Motion diagrams: horizontal motion A car moves to the right. For an initial period it slows down and after that it speeds up. Which of

### 1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D

Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be

### B) 286 m C) 325 m D) 367 m Answer: B

Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of

### Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

### Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region

### Homework #8 203-1-1721 Physics 2 for Students of Mechanical Engineering. Part A

Homework #8 203-1-1721 Physics 2 for Students of Mechanical Engineering Part A 1. Four particles follow the paths shown in Fig. 32-33 below as they pass through the magnetic field there. What can one conclude

I. A mechanical device shakes a ball-spring system vertically at its natural frequency. The ball is attached to a string, sending a harmonic wave in the positive x-direction. +x a) The ball, of mass M,

### questions: force and motion I

questions: force and motion I problem 1 The figure below is an overhead view of a 12 kg tire that is to be pulled by three ropes. One force (F l, with magnitude 50 N) is indicated. Orient the other two

### Chapter 4: Newton s Laws: Explaining Motion

Chapter 4: Newton s Laws: Explaining Motion 1. All except one of the following require the application of a net force. Which one is the exception? A. to change an object from a state of rest to a state

### 1. Newton s Laws of Motion and their Applications Tutorial 1

1. Newton s Laws of Motion and their Applications Tutorial 1 1.1 On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0

### EXPERIMENT: MOMENT OF INERTIA

OBJECTIVES EXPERIMENT: MOMENT OF INERTIA to familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body as mass plays in

### Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t

Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a load-carrying

### Chapter 11 Equilibrium

11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of

### Chapter 13, example problems: x (cm) 10.0

Chapter 13, example problems: (13.04) Reading Fig. 13-30 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.

### Problem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s

Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to

### Newton s Third Law. object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1

Newton s Third Law! If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1!! Note on notation: is

### If you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ

Experiment 4 ormal and Frictional Forces Preparation Prepare for this week's quiz by reviewing last week's experiment Read this week's experiment and the section in your textbook dealing with normal forces

### Chapter 19 Magnetic Forces and Fields

Chapter 19 Magnetic Forces and Fields Student: 3. The magnetism of the Earth acts approximately as if it originates from a huge bar magnet within the Earth. Which of the following statements are true?