Question 1

A child is riding a merry-go-round that is turning at 7.18 rpm.If the child is standing 4.65 m from the center of the merry-go-round,how fast is the child moving?

Accepted Answer

A) 5.64 m/s 
B) 3.50 m/s 
C) 0.556 m/s 
D) 1.75 m/s 
E) 1.80 m/s 
A) 5.64 m/s 
B) 3.50 m/s 
C) 0.556 m/s 
D) 1.75 m/s 
E) 1.80 m/s B

Question 2

The drive chain in a bicycle is exerting a torque of 0.850 N ∙ m to the wheel of the bicycle.The wheel has a moment of inertia of 0.100 kg ∙ m2.What is the angular acceleration of the wheel?

Accepted Answer

8.50 rad/s²

Question 3

When Mary is 3.00 m from the center of a merry-go-round,her tangential speed is a constant 1.88 m/s.
(a)What is her angular speed in rad/s?
(b)What is the magnitude of her linear acceleration?

Accepted Answer

(a)0.627 rad/s (b)1.18 m/s²

Question 4

A solid wood door,90.0 cm wide by 2.00 m tall has a mass of 35.0 kg.It is open and at rest.A small 500-g ball is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side.The ball rebounds with a speed of 16.0 m/s along the same line.What is the angular speed of the door just after the collision with the ball?

Accepted Answer

A) 0.127 rad/s 
B) 0.925 rad/s 
C) 1.14 rad/s 
D) 2.28 rad/s 
E) 4.57 rad/s 
A) 0.127 rad/s 
B) 0.925 rad/s 
C) 1.14 rad/s 
D) 2.28 rad/s 
E) 4.57 rad/s

Question 5

An ice skater has a moment of inertia of 5.0 kg ∙ m2 when her arms are outstretched,and at this time she is spinning at 3.0 rev/s.If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m2,how fast will she be spinning?

Accepted Answer

A) 2.0 rev/s 
B) 3.3 rev/s 
C) 7.5 rev/s 
D) 10 rev/s 
A) 2.0 rev/s 
B) 3.3 rev/s 
C) 7.5 rev/s 
D) 10 rev/s

Question 6

A disk,a hoop,and a solid sphere are released at the same time at the top of an inclined plane.They are all uniform and roll without slipping.In what order do they reach the bottom?

Accepted Answer

A) disk, hoop, sphere 
B) hoop, sphere, disk 
C) sphere, disk, hoop 
D) sphere, hoop, disk 
E) hoop, disk, sphere 
A) disk, hoop, sphere 
B) hoop, sphere, disk 
C) sphere, disk, hoop 
D) sphere, hoop, disk 
E) hoop, disk, sphere

Question 7

A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s.What is the magnitude of the angular momentum of the stick?

Accepted Answer

A) 0.0394 kg ∙ m2/s 
B) 0.473 kg ∙ m2/s 
C) 0.0739 kg ∙ m2/s 
D) 0.158 kg ∙ m2/s 
E) 0.0236 kg ∙ m2/s 
A) 0.0394 kg ∙ m2/s 
B) 0.473 kg ∙ m2/s 
C) 0.0739 kg ∙ m2/s 
D) 0.158 kg ∙ m2/s 
E) 0.0236 kg ∙ m2/s

Question 8

While spinning down from 500 rpm to rest,a flywheel does $3.9 \mathrm {~kJ}$ of work.This flywheel is in the shape of a solid uniform disk of radius 1.2 m.What is the mass of this flywheel?

Accepted Answer

A) 4.0 kg 
B) 3.4 kg 
C) 4.6 kg 
D) 5.2 kg 
A) 4.0 kg 
B) 3.4 kg 
C) 4.6 kg 
D) 5.2 kg

Question 9

A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of $0.0125 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ and a radius of 15.0 cm.A mass of 710 g hangs from the other end of the string.When the tiles are released,the larger one accelerates downward while the lighter one accelerates upward.The pulley has no friction in its axle and turns without the string slipping.What is the tension in the string on the side of the 710-g tile?

Accepted Answer

A) 9.77 N 
B) 6.87 N 
C) 5.59 N 
D) 4.41 N 
E) 3.68 N 
A) 9.77 N 
B) 6.87 N 
C) 5.59 N 
D) 4.41 N 
E) 3.68 N

Question 10

A triatomic molecule is oriented as follows along the x-axis: atom 1 of mass m is at the origin,atom 2 of mass 2m is at x = a,and,atom 3 of mass 3m is at x = 2a.What is the moment of inertia of this molecule about the y-axis?

Accepted Answer

A) 2ma2 
B) 3ma2 
C) 12ma2 
D) 14ma2 
A) 2ma2 
B) 3ma2 
C) 12ma2 
D) 14ma2

Question 11

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

Accepted Answer

A) her moment of inertia decreases and her angular speed increases. 
B) her moment of inertia decreases and her angular speed decreases. 
C) her moment of inertia increases and her angular speed increases. 
D) her moment of inertia increases and her angular speed decreases. 
E) her moment of inertia increases and her angular speed remains the same. 
A) her moment of inertia decreases and her angular speed increases. 
B) her moment of inertia decreases and her angular speed decreases. 
C) her moment of inertia increases and her angular speed increases. 
D) her moment of inertia increases and her angular speed decreases. 
E) her moment of inertia increases and her angular speed remains the same.

Question 12

As shown in the figure,two blocks are connected by a light string that passes over a frictionless pulley having a moment of inertia of 0.0040 kg ∙ m2 and diameter 10 cm.The coefficient of kinetic friction between the table top and the upper block is 0.30.The blocks are released from rest,and the string does not slip on the pulley.How fast is the upper block moving when the lower one has fallen 0.60 m?

Accepted Answer

A) 1.2 m/s 
B) 5.4 m/s 
C) 3.2 m/s 
D) 2.0 m/s 
E) 1.4 m/s 
A) 1.2 m/s 
B) 5.4 m/s 
C) 3.2 m/s 
D) 2.0 m/s 
E) 1.4 m/s

Question 13

The L-shaped object shown in the figure consists of three small mass objects connected by thin uniform rods,each rod of mass 3.00 kg.Assume that the masses shown are accurate to three significant figures.How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the y-axis?

Accepted Answer

The answer of The L-shaped object shown in the figure...

Question 14

A majorette fastens two batons together at their centers to form an X shape.Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end.What is the moment of inertia of this baton about an axis through the center of the X?

Accepted Answer

The answer of A majorette fastens two batons together at...

Question 15

Initially,a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface,as shown in the figure.The initial tangential speed of the rock was 5.0 m/s.The string has been slowly winding around a vertical rod,and a few seconds later the length of the string has shortened to 0.25 m.What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m?

Accepted Answer

A) 3.9 m/s 
B) 9.3 m/s 
C) 15 m/s 
D) 225 m/s 
E) 75 m/s 
A) 3.9 m/s 
B) 9.3 m/s 
C) 15 m/s 
D) 225 m/s 
E) 75 m/s

Question 16

A 40.0-kg child running at 3.00 m/s suddenly jumps onto a stationary playground merry-go-round at a distance 1.50 m from the axis of rotation of the merry-go-round.The child is traveling tangential to the edge of the merry-go-round just before jumping on.The moment of inertia about its axis of rotation is 600 kg ∙ m2 and very little friction at its rotation axis.What is the angular speed of the merry-go-round just after the child has jumped onto it?

Accepted Answer

A) 0.788 rad/s 
B) 0.261 rad/s 
C) 6.28 rev/s 
D) 2.00 rad/s 
E) 3.14 rev/s 
A) 0.788 rad/s 
B) 0.261 rad/s 
C) 6.28 rev/s 
D) 2.00 rad/s 
E) 3.14 rev/s

Question 17

The L-shaped object shown in the figure consists of three small mass spheres connected by extremely light rods.Assume that the masses shown are accurate to three significant figures.What is the moment of inertia of this object (a)about the x-axis,and (b)about the y-axis?

Accepted Answer

(a)6.48 kg

Question 18

The diameter of the Moon is 3.47 × 106 m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?

Accepted Answer

Question 19

A spinning ice skater is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)

Accepted Answer

A) Her angular momentum remains almost constant. 
B) Her moment of inertia remains almost constant. 
C) Her kinetic energy remains almost constant. 
D) She is subject to a constant non-zero torque. 
A) Her angular momentum remains almost constant. 
B) Her moment of inertia remains almost constant. 
C) Her kinetic energy remains almost constant. 
D) She is subject to a constant non-zero torque.

Question 20

A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal.What is the forward speed of the disk after it has rolled 3.0 m,measured along the plane?

Accepted Answer

A) 2.0 m/s 
B) 3.5 m/s 
C) 4.1 m/s 
D) 5.7 m/s 
E) 6.3 m/s 
A) 2.0 m/s 
B) 3.5 m/s 
C) 4.1 m/s 
D) 5.7 m/s 
E) 6.3 m/s

Exam 9: Rotational Motion

A child is riding a merry-go-round that is turning at 7.18 rpm.If the child is standing 4.65 m from the center of the merry-go-round,how fast is the child moving?

The drive chain in a bicycle is exerting a torque of 0.850 N ∙ m to the wheel of the bicycle.The wheel has a moment of inertia of 0.100 kg ∙ m2.What is the angular acceleration of the wheel?

When Mary is 3.00 m from the center of a merry-go-round,her tangential speed is a constant 1.88 m/s. (a)What is her angular speed in rad/s? (b)What is the magnitude of her linear acceleration?

An ice skater has a moment of inertia of 5.0 kg ∙ m2 when her arms are outstretched,and at this time she is spinning at 3.0 rev/s.If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m2,how fast will she be spinning?

A disk,a hoop,and a solid sphere are released at the same time at the top of an inclined plane.They are all uniform and roll without slipping.In what order do they reach the bottom?

A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s.What is the magnitude of the angular momentum of the stick?

While spinning down from 500 rpm to rest,a flywheel does 3.9 kJ3.9 \mathrm {~kJ}3.9 kJ of work.This flywheel is in the shape of a solid uniform disk of radius 1.2 m.What is the mass of this flywheel?

A triatomic molecule is oriented as follows along the x-axis: atom 1 of mass m is at the origin,atom 2 of mass 2m is at x = a,and,atom 3 of mass 3m is at x = 2a.What is the moment of inertia of this molecule about the y-axis?

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

A majorette fastens two batons together at their centers to form an X shape.Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end.What is the moment of inertia of this baton about an axis through the center of the X?

The L-shaped object shown in the figure consists of three small mass spheres connected by extremely light rods.Assume that the masses shown are accurate to three significant figures.What is the moment of inertia of this object (a)about the x-axis,and (b)about the y-axis?

The diameter of the Moon is 3.47 × 106 m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?

A spinning ice skater is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)

A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal.What is the forward speed of the disk after it has rolled 3.0 m,measured along the plane?

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

The drive chain in a bicycle is exerting a torque of 0.850 N ∙ m to the wheel of the bicycle.The wheel has a moment of inertia of 0.100 kg ∙ m².What is the angular acceleration of the wheel?

An ice skater has a moment of inertia of 5.0 kg ∙ m² when her arms are outstretched,and at this time she is spinning at 3.0 rev/s.If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m²,how fast will she be spinning?

While spinning down from 500 rpm to rest,a flywheel does $3.9 \mathrm {~kJ}$ of work.This flywheel is in the shape of a solid uniform disk of radius 1.2 m.What is the mass of this flywheel?

The diameter of the Moon is 3.47 × 10⁶ m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?