Question 1

The angular momentum of a system is conserved only if

Accepted Answer

A) the angular velocity is a function of time. 
B) the sum of the external torques equals the sum of the internal torques. 
C) the moment of inertia of the system is constant. 
D) the sum of the external torques is zero. 
E) the sum of the internal torques is zero. 
A) the angular velocity is a function of time. 
B) the sum of the external torques equals the sum of the internal torques. 
C) the moment of inertia of the system is constant. 
D) the sum of the external torques is zero. 
E) the sum of the internal torques is zero.

Question 2

In a rotating atomic nucleus shaped like a football the quantized rotational energy levels have angular momentum values l = 0,2,4,6,8,etc.Given that the energy of each level is equal to a constant times l $\times$ (l + 1),calculate the ratio of the l = 4 to l = 2 energy levels.

Accepted Answer

A) 4.0 
B) 0.3 
C) 2.0 
D) 0.5 
E) 3.3 
A) 4.0 
B) 0.3 
C) 2.0 
D) 0.5 
E) 3.3

Question 3

Particles 1,2,and 3 have equal masses and equal speeds.The angular momentum with respect to the origin for these three masses is

Accepted Answer

A) the same for each particle. 
B) greatest for particle 1. 
C) greatest for particle 2. 
D) greatest for particle 3. 
E) least for particle 2. 
A) the same for each particle. 
B) greatest for particle 1. 
C) greatest for particle 2. 
D) greatest for particle 3. 
E) least for particle 2.

Question 4

In a playground there is a small merry-go-round of radius 1.25 m and mass 175 kg.Assume the merry-go-round to be a uniform disc.A child of mass 45 kg runs at a speed of 3.0 m/s tangent to the rim of the merry-go-round (initially at rest)and jumps on.If we neglect friction,what is the angular speed of the merry-go-round after the child has jumped on and is standing at its outer rim?

Accepted Answer

A) 0.82 rad/s 
B) 2.4 rad/s 
C) 0.49 rad/s 
D) 1.2 rad/s 
E) 0.41 rad/s 
A) 0.82 rad/s 
B) 2.4 rad/s 
C) 0.49 rad/s 
D) 1.2 rad/s 
E) 0.41 rad/s

Question 5

A solid cylinder is spinning counterclockwise about a longitudinal axis when a net torque $\tau$ is applied,as shown.The cylinder

Accepted Answer

A) speeds up. 
B) slows down. 
C) precesses about a vertical axis. 
D) precesses about a horizontal axis. 
E) does none of these. 
A) speeds up. 
B) slows down. 
C) precesses about a vertical axis. 
D) precesses about a horizontal axis. 
E) does none of these.

Question 6

The figure shows vectors representing the angular velocity of precession $\omega$p and the spin velocity $\omega$s.The associated torque vector points along which of the axes?

Accepted Answer

A) -x 
B) y 
C) z 
D) -z 
E) None of these is correct. 
A) -x 
B) y 
C) z 
D) -z 
E) None of these is correct.

Question 7

A wheel is rotating freely with an angular speed of 20 rad/s on a shaft whose moment of inertia is negligible.A second identical wheel,initially at rest,is suddenly coupled to the same shaft.The angular speed of the coupled wheels is

Accepted Answer

A) 10 rad/s 
B) 14 rad/s 
C) 20 rad/s 
D) 28 rad/s 
E) 40 rad/s 
A) 10 rad/s 
B) 14 rad/s 
C) 20 rad/s 
D) 28 rad/s 
E) 40 rad/s

Question 8

A torque is applied to a bolt by hanging a weight w from the end of the wrench,as shown.The coordinate axis along which the torque vector is directed is

Accepted Answer

A) y 
B) x 
C) -y 
D) -x 
E) z 
A) y 
B) x 
C) -y 
D) -x 
E) z

Question 9

In a rotating atomic nucleus shaped like a football the quantized energy levels have rotational quantum number values of 0,2,4,etc.If the energies of the first three states are 0 keV,138 keV,and 460 keV,calculate the moment of inertia of the nucleus.

Accepted Answer

A) 9.41 $\times$ 10-36 keV•s2  
B) 9.41 $\times$ 10-36 eV•s2  
C) 1.43 $\times$10-17 keV•s2  
D) 1.43 $\times$ 10-17 eV•s2  
E) 9.41 $\times$10-33 keV•s2  
A) 9.41 $\times$ 10-36 keV•s2  
B) 9.41 $\times$ 10-36 eV•s2  
C) 1.43 $\times$10-17 keV•s2  
D) 1.43 $\times$ 10-17 eV•s2  
E) 9.41 $\times$10-33 keV•s2

Question 10

Which of the following statements is true?

Accepted Answer

A) Stable matter consists of electrons,protons,and neutrons. 
B) Electrons,protons,and neutrons have an intrinsic angular momentum that is called spin. 
C) Bosons have zero spin or integral spin. 
D) The spin angular momentum of a particle is a fundamental property of the particle and as such cannot be changed. 
E) All of these are correct. 
A) Stable matter consists of electrons,protons,and neutrons. 
B) Electrons,protons,and neutrons have an intrinsic angular momentum that is called spin. 
C) Bosons have zero spin or integral spin. 
D) The spin angular momentum of a particle is a fundamental property of the particle and as such cannot be changed. 
E) All of these are correct.

Question 11

For a rotating molecule with a constant moment of inertia what is the energy difference between the l = 5 and l = 7 energy levels?

Accepted Answer

A) 2 E0r  
B) 24 E0r 
C) 86 E0r 
D) 26 E0r 
E) 35 E0r 
A) 2 E0r  
B) 24 E0r 
C) 86 E0r 
D) 26 E0r 
E) 35 E0r

Question 12

The angular momentum vector for a spinning wheel lies along its axle and is pointed east.To make this vector point south,it is necessary to exert a force on the east end of the axle in which direction?

Accepted Answer

A) up 
B) down 
C) north 
D) south 
E) east 
A) up 
B) down 
C) north 
D) south 
E) east

Question 13

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum   0 and she turns it over (that is,through 180º).She thereby acquires an angular momentum of magnitude

Accepted Answer

A) 0 
B)      0  
C)    0  
D) 2   0 
E) 4   0  
A) 0 
B)      0  
C)    0  
D) 2   0 
E) 4   0

Question 14

Use the figure to the right to answer the next  problem. A ball of mass of mass m is tied with a light string to a vertical post of radius RS1U1B1pS1U1B0 and slides on a frictionless horizontal surface. As the ball travels around the post, the string wraps around the post, shortening the length. At t = 0 s, its speed is vS1U1B1oS1U1B0 and radius is rS1U1B1oS1U1B0. 
 
-As the string wraps around the post,which of the following statements is true?

Accepted Answer

A) Angular momentum is conserved but not the mechanical energy. 
B) Angular momentum is not conserved but the mechanical energy is conserved. 
C) Both the angular momentum and the mechanical energy are conserved. 
D) Angular momentum increases as the string gets shorter. 
E) Whether the angular momentum and mechanical energy are conserved depends on vo and ro. 
A) Angular momentum is conserved but not the mechanical energy. 
B) Angular momentum is not conserved but the mechanical energy is conserved. 
C) Both the angular momentum and the mechanical energy are conserved. 
D) Angular momentum increases as the string gets shorter. 
E) Whether the angular momentum and mechanical energy are conserved depends on vo and ro.

Question 15

An athletic can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s.If the length of a uniform baton is 0.8 m and the mass is 0.5 kg,what is the torque needed to reach the angular velocity?

Accepted Answer

A) 0.4 N.m 
B) 0.5 N.m 
C) 0.8 N.m 
D) 0.64 N.m 
E) 1.24 N.m 
A) 0.4 N.m 
B) 0.5 N.m 
C) 0.8 N.m 
D) 0.64 N.m 
E) 1.24 N.m

Question 16

Spin   particles

Accepted Answer

A) are called bosons. 
B) have spin angular momenta that can be changed by applying a net torque to them. 
C) can have angular momenta that change continuously from one value to another. 
D) can very accurately be thought of as spinning spheres. 
E) are described by none of the above. 
A) are called bosons. 
B) have spin angular momenta that can be changed by applying a net torque to them. 
C) can have angular momenta that change continuously from one value to another. 
D) can very accurately be thought of as spinning spheres. 
E) are described by none of the above.

Question 17

If an object were to suddenly shrink and decrease its moment of inertia by a factor of 3,what is the difference in energy between the final and initial rotational kinetic energies?

Accepted Answer

A) 3 times initial Krot  
B) 9 times initial Krot  
C) 8 times initial Krot  
D) 2 times initial Krot  
E) zero,Krot remains the same 
A) 3 times initial Krot  
B) 9 times initial Krot  
C) 8 times initial Krot  
D) 2 times initial Krot  
E) zero,Krot remains the same

Question 18

A 7-kg mass and a 4-kg mass are mounted on a spindle that is free to turn about the x axis as shown.Assume the mass of the arms and the spindle to be negligible.If the system is free to rotate and is released from rest,there will initially be a resultant torque in which of the following directions?

Accepted Answer

A) z 
B) -z 
C) y 
D) -x 
E) x 
A) z 
B) -z 
C) y 
D) -x 
E) x

Question 19

A wheel is set spinning and is then hung by a rope placed at one end of the axle.If the wheel is spinning as shown,the angular momentum of the wheel could be represented by vector

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

A man turns with an angular velocity on a rotating table,holding two equal masses at arms' length.If he drops the two masses without moving his arms,his angular velocity

Accepted Answer

A) decreases. 
B) remains the same. 
C) increases. 
D) increases as the angular velocity of the masses decreases. 
E) decreases as the angular velocity of the masses increases. 
A) decreases. 
B) remains the same. 
C) increases. 
D) increases as the angular velocity of the masses decreases. 
E) decreases as the angular velocity of the masses increases.

Exam 10: Conservation of Angular Momentum

The angular momentum of a system is conserved only if

In a rotating atomic nucleus shaped like a football the quantized rotational energy levels have angular momentum values l = 0,2,4,6,8,etc.Given that the energy of each level is equal to a constant times l ×\times× (l + 1),calculate the ratio of the l = 4 to l = 2 energy levels.

Particles 1,2,and 3 have equal masses and equal speeds.The angular momentum with respect to the origin for these three masses is

A solid cylinder is spinning counterclockwise about a longitudinal axis when a net torque τ\tauτ is applied,as shown.The cylinder

The figure shows vectors representing the angular velocity of precession ω\omegaω p and the spin velocity ω\omegaω s.The associated torque vector points along which of the axes?

A wheel is rotating freely with an angular speed of 20 rad/s on a shaft whose moment of inertia is negligible.A second identical wheel,initially at rest,is suddenly coupled to the same shaft.The angular speed of the coupled wheels is

A torque is applied to a bolt by hanging a weight w from the end of the wrench,as shown.The coordinate axis along which the torque vector is directed is

In a rotating atomic nucleus shaped like a football the quantized energy levels have rotational quantum number values of 0,2,4,etc.If the energies of the first three states are 0 keV,138 keV,and 460 keV,calculate the moment of inertia of the nucleus.

Which of the following statements is true?

For a rotating molecule with a constant moment of inertia what is the energy difference between the l = 5 and l = 7 energy levels?

The angular momentum vector for a spinning wheel lies along its axle and is pointed east.To make this vector point south,it is necessary to exert a force on the east end of the axle in which direction?

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum 0 and she turns it over (that is,through 180º).She thereby acquires an angular momentum of magnitude

An athletic can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s.If the length of a uniform baton is 0.8 m and the mass is 0.5 kg,what is the torque needed to reach the angular velocity?

Spin particles

If an object were to suddenly shrink and decrease its moment of inertia by a factor of 3,what is the difference in energy between the final and initial rotational kinetic energies?

A 7-kg mass and a 4-kg mass are mounted on a spindle that is free to turn about the x axis as shown.Assume the mass of the arms and the spindle to be negligible.If the system is free to rotate and is released from rest,there will initially be a resultant torque in which of the following directions?

A wheel is set spinning and is then hung by a rope placed at one end of the axle.If the wheel is spinning as shown,the angular momentum of the wheel could be represented by vector

A man turns with an angular velocity on a rotating table,holding two equal masses at arms' length.If he drops the two masses without moving his arms,his angular velocity

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In a rotating atomic nucleus shaped like a football the quantized rotational energy levels have angular momentum values l = 0,2,4,6,8,etc.Given that the energy of each level is equal to a constant times l $\times$ (l + 1),calculate the ratio of the l = 4 to l = 2 energy levels.

A solid cylinder is spinning counterclockwise about a longitudinal axis when a net torque $\tau$ is applied,as shown.The cylinder $A solid cylinder is spinning counterclockwise about a longitudinal axis when a net torque \tau is applied,as shown.The cylinder$

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum ₀ and she turns it over (that is,through 180º).She thereby acquires an angular momentum of magnitude