Question 1

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm.What is the magnitude of the angular acceleration of the record?

Accepted Answer

A) 2.34 rad/s2 
B) 5.46 rad/s2 
C) 6.50 rad/s2 
D) 8.35 rad/s2 
E) 10.9 rad/s2 
A) 2.34 rad/s2 
B) 5.46 rad/s2 
C) 6.50 rad/s2 
D) 8.35 rad/s2 
E) 10.9 rad/s2

Question 2

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane,and they roll down without slipping.Which one will reach the bottom first?

Accepted Answer

A) the one of smallest diameter 
B) the one of greatest mass 
C) the disk 
D) the sphere 
E) They will reach the bottom at the same time. 
A) the one of smallest diameter 
B) the one of greatest mass 
C) the disk 
D) the sphere 
E) They will reach the bottom at the same time.

Question 3

A 375-g stone hangs from a thin light string that is wrapped around the circumference of a frictionless pulley with a moment of inertia of 0.0125 kg ∙ m2 and a radius of 26 cm.When the stone is released,the stone accelerates downward and the pulley rotates about its axis as the string unwinds.
(a)What is the magnitude of the acceleration of the stone?
(b)What is the force that the string exerts on the stone?

Accepted Answer

(a)6.6 m/s

Question 4

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s2.How many revolutions does it make while slowing down before coming to rest?

Accepted Answer

A) 40 
B) 20 
C) 6.4 
D) 3.2 
A) 40 
B) 20 
C) 6.4 
D) 3.2

Question 5

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m2 is rotating freely with an angular speed of 1.0 rad/s.Two people,each of mass 60 kg,are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground.What is the angular speed of the merry-go-round right after the two people have stepped on?

Accepted Answer

A) 0.20 rad/s 
B) 0.40 rad/s 
C) 0.60 rad/s 
D) 0.80 rad/s 
E) 0.67 rad/s 
A) 0.20 rad/s 
B) 0.40 rad/s 
C) 0.60 rad/s 
D) 0.80 rad/s 
E) 0.67 rad/s

Question 6

A force of $16.88 \mathrm {~N}$ is exerted tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2.What is the moment of inertia of the wheel?

Accepted Answer

A) 4.78 kg ∙ m2 
B) 3.59 kg ∙ m2 
C) 5.98 kg ∙ m2 
D) 7.17 kg ∙ m2 
A) 4.78 kg ∙ m2 
B) 3.59 kg ∙ m2 
C) 5.98 kg ∙ m2 
D) 7.17 kg ∙ m2

Question 7

A solid sphere and a solid cylinder,both uniform and of the same mass and radius,roll without slipping at the same forward speed.It is correct to say that the total kinetic energy of the solid sphere is

Accepted Answer

A) more than the total kinetic energy of the cylinder. 
B) less than the total kinetic energy of the cylinder. 
C) equal to the total kinetic energy of the cylinder. 
A) more than the total kinetic energy of the cylinder. 
B) less than the total kinetic energy of the cylinder. 
C) equal to the total kinetic energy of the cylinder.

Question 8

A car is traveling along a freeway at 65 mph.What is the linear speed,relative to the highway,of each of the following points on one of its tires?
(a)the highest point on the tire
(b)the lowest point on a tire
(c)the center of the tire

Accepted Answer

(a)130 mph

Question 9

Two uniform solid spheres have the same mass,but one has twice the radius of the other.The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is

Accepted Answer

A) 4/5. 
B) 8/5. 
C) 1/2. 
D) 2. 
E) 4. 
A) 4/5. 
B) 8/5. 
C) 1/2. 
D) 2. 
E) 4.

Question 10

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii.If the three of them are released simultaneously at the top of an inclined plane and do not slip,which one will reach the bottom first?

Accepted Answer

A) sphere 
B) pipe 
C) cylinder 
D) The pipe and cylinder arrive together before the sphere. 
E) They all reach the bottom at the same time. 
A) sphere 
B) pipe 
C) cylinder 
D) The pipe and cylinder arrive together before the sphere. 
E) They all reach the bottom at the same time.

Question 11

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping.Through how many degrees does the cylinder turn during this time?

Accepted Answer

The answer of A cylinder of radius 8.0 cm rolls...

Question 12

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

Accepted Answer

A) 11 rad/s 
B) 22 rad/s 
C) 45 rad/s 
D) 69 rad/s 
E) 660 rad/s 
A) 11 rad/s 
B) 22 rad/s 
C) 45 rad/s 
D) 69 rad/s 
E) 660 rad/s

Question 13

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O,as shown in the cross-sectional view in the figure.A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right.A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward.How many radians does the cylinder rotate through in the first 5.0 seconds,if it starts from rest?

Accepted Answer

A) 13 rad 
B) 7.5 rad 
C) 5.0 rad 
D) 10 rad 
A) 13 rad 
B) 7.5 rad 
C) 5.0 rad 
D) 10 rad

Question 14

In a laboratory experiment,a student brings up the rotational speed of a flywheel to 30.0 rpm.She then allows it to slow down on its own,and counts 240 revolutions before the apparatus uniformly comes to a stop.The moment of inertia of the flywheel is 0.0850 kg ∙ m2.What is the magnitude of the retarding torque on the flywheel?

Accepted Answer

A) 0.0425 N ∙ m 
B) 0.159 N ∙ m 
C) 0.0787 N ∙ m 
D) 0.000278 N ∙ m 
E) 0.0000136 N ∙ m 
A) 0.0425 N ∙ m 
B) 0.159 N ∙ m 
C) 0.0787 N ∙ m 
D) 0.000278 N ∙ m 
E) 0.0000136 N ∙ m

Question 15

A 350-g air track cart on a horizontal air track is attached to a string that goes over a frictionless pulley with a moment of inertia of 6.00 × 10-6 kg ∙ m2 and a radius of 1.35 cm.If the string is pulled vertically downward by a force of 2.50 N,(a)what is the magnitude of the acceleration of the cart,and (b)what is the force that the horizontal string between the pulley and the cart exerts on the cart?

Accepted Answer

(a)6.53 m/

Question 16

A 24.5-kg child is standing on the outer edge of a horizontal merry-go-round that has a moment of inertia of $989 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ about a vertical axis through its center and a radius of 2.40 m.The entire system (including the child)is initially rotating at 0.180 rev/s.Find the angular velocity if the child moves to a new position 1.10 m from the center of the merry-go-round.

Accepted Answer

The answer of A 24.5-kg child is standing on the...

Question 17

The drum shown in the figure has a radius of 0.40 m and a moment of inertia of 2.3 $\mathrm { kg } \cdot \mathrm { m } ^ { 2 }$ about an axis perpendicular to it through its center.The frictional torque at the drum axle is 3.0 N ∙ m.A 14-m length of rope is wound around the rim.The drum is initially at rest.A constant force is exerted on the free end of the rope until the rope is completely unwound and slips off.At that instant,the angular speed of the drum is $23 \mathrm { rad } / \mathrm { s }$ The drum then slows down at a constant rate and comes to a halt.In this situation,what was the magnitude of the constant force that pulled the rope?

Accepted Answer

A) 51 N 
B) 40 N 
C) 29 N 
D) 18 N 
E) 7.5 N 
A) 51 N 
B) 40 N 
C) 29 N 
D) 18 N 
E) 7.5 N

Question 18

A torque of 12 N ∙ m is exerted on a solid,uniform disk of radius 0.50 m.If the disk accelerates at $1.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$ what is the mass of the disk?

Accepted Answer

A) 60 kg 
B) 45 kg 
C) 30 kg 
D) 15 kg 
A) 60 kg 
B) 45 kg 
C) 30 kg 
D) 15 kg

Question 19

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2.Through what angle does the pulley turn in 5.26 s?

Accepted Answer

A) 113 rad 
B) 22.6 rad 
C) 42.6 rad 
D) 19.3 rad 
E) 160 rad 
A) 113 rad 
B) 22.6 rad 
C) 42.6 rad 
D) 19.3 rad 
E) 160 rad

Question 20

A wheel accelerates from rest to $59 \mathrm { rad } / \mathrm { s }$ at a uniform rate of 58 rad/s2. Through what angle (in radians)did the wheel turn while accelerating?

Accepted Answer

A) 30 rad 
B) 24 rad 
C) 60 rad 
D) 38 rad 
A) 30 rad 
B) 24 rad 
C) 60 rad 
D) 38 rad

Exam 9: Rotational Motion

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm.What is the magnitude of the angular acceleration of the record?

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane,and they roll down without slipping.Which one will reach the bottom first?

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s2.How many revolutions does it make while slowing down before coming to rest?

A force of 16.88 N16.88 \mathrm {~N}16.88 N is exerted tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2.What is the moment of inertia of the wheel?

A solid sphere and a solid cylinder,both uniform and of the same mass and radius,roll without slipping at the same forward speed.It is correct to say that the total kinetic energy of the solid sphere is

A car is traveling along a freeway at 65 mph.What is the linear speed,relative to the highway,of each of the following points on one of its tires? (a)the highest point on the tire (b)the lowest point on a tire (c)the center of the tire

Two uniform solid spheres have the same mass,but one has twice the radius of the other.The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii.If the three of them are released simultaneously at the top of an inclined plane and do not slip,which one will reach the bottom first?

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping.Through how many degrees does the cylinder turn during this time?

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

A torque of 12 N ∙ m is exerted on a solid,uniform disk of radius 0.50 m.If the disk accelerates at 1.6rad/s21.6 \mathrm { rad } / \mathrm { s } ^ { 2 }1.6rad/s2 what is the mass of the disk?

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2.Through what angle does the pulley turn in 5.26 s?

A wheel accelerates from rest to 59rad/s59 \mathrm { rad } / \mathrm { s }59rad/s at a uniform rate of 58 rad/s2. Through what angle (in radians)did the wheel turn while accelerating?

Introduction

Kinematics: Motion in One Dimension

Newtonian Mechanics

Applying Newtons Laws

Circular Motion

Impulse and Linear Momentum

Work and Energy

Extended Bodies at Rest

Gases

Static Fluids

Fluids in Motion

First Law of Thermodynamics

Second Law of Thermodynamics

Electric Charge force and Energy

The Electric Field

Dc Circuits

Magnetism

Electromagnetic Induction

Vibrational Motion

Mechanical Waves

Reflection and Refraction

Mirrors and Lenses

Wave Optics

Electromagnetic Waves

Special Relativity

Quantum Optics

Atomic Physics

Nuclear Physics

Particle Physics

Filters

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s².How many revolutions does it make while slowing down before coming to rest?

A force of $16.88 \mathrm {~N}$ is exerted tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s².What is the moment of inertia of the wheel?

A torque of 12 N ∙ m is exerted on a solid,uniform disk of radius 0.50 m.If the disk accelerates at $1.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$ what is the mass of the disk?

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s².Through what angle does the pulley turn in 5.26 s?

A wheel accelerates from rest to $59 \mathrm { rad } / \mathrm { s }$ at a uniform rate of 58 rad/s²_. Through what angle (in radians)did the wheel turn while accelerating?