Question 1

A constant torque of 15 N · m acts for 3.0 s on a system of mass 2.0 kg. The change in angular momentum of the system during this period of time is

Accepted Answer

A)  5.0 kg · m2/s 
B)  7.5 kg · m2/s 
C)  10 kg · m2/s 
D)  23 kg · m2/s 
E)  45 kg · m2/s 
A)  5.0 kg · m2/s 
B)  7.5 kg · m2/s 
C)  10 kg · m2/s 
D)  23 kg · m2/s 
E)  45 kg · m2/s

Question 2

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 3

A woman sits on a spinning piano stool with her arms folded. When she extends her arms, which of the following occurs?

Accepted Answer

A)  She increases her moment of inertia, thereby increasing her angular speed. 
B)  She increases her moment of inertia, thereby decreasing her angular speed. 
C)  She decreases her moment of inertia, thereby increasing her angular speed. 
D)  She decreases her moment of inertia, thereby decreasing her angular speed. 
E)  Both her moment of inertia and her angular speed remain constant. 
A)  She increases her moment of inertia, thereby increasing her angular speed. 
B)  She increases her moment of inertia, thereby decreasing her angular speed. 
C)  She decreases her moment of inertia, thereby increasing her angular speed. 
D)  She decreases her moment of inertia, thereby decreasing her angular speed. 
E)  Both her moment of inertia and her angular speed remain constant.

Question 4

If the distance between two hydrogen atoms of H2 is 0.1 nm, what is its E0r?

Accepted Answer

A)  2.40 $\times$ 10-23 J 
B)  6.70 $\times$ 10-22 J 
C)  1.05 $\times$ 10-22 J 
D)  1.60 $\times$ 10-22 J 
E)  2.45 $\times$ 10-22 J 
A)  2.40 $\times$ 10-23 J 
B)  6.70 $\times$ 10-22 J 
C)  1.05 $\times$ 10-22 J 
D)  1.60 $\times$ 10-22 J 
E)  2.45 $\times$ 10-22 J

Question 5

Large meteors can impact the earth with speeds of 80,000 km/h. If such a meteor were to impact at a point on the plane of Earth's equator, resulting in a change of Earth's angular momentum by 80 × 1012 kg • m2/s (an insignificant change, thankfully), calculate the mass of the meteor. (The radius of Earth = 6.38 $\times$ 106 m.)

Accepted Answer

A)  3.4 $\times$ 104 kg 
B)  5.6 $\times$ 102 kg 
C)  3.6 $\times$ 103 kg 
D)  4.5 $\times$ 104 kg 
E)  56 kg 
A)  3.4 $\times$ 104 kg 
B)  5.6 $\times$ 102 kg 
C)  3.6 $\times$ 103 kg 
D)  4.5 $\times$ 104 kg 
E)  56 kg

Question 6

A particle of mass m is moving with a velocity   , in the yz plane as shown. The vector that most nearly represents the angular momentum about the x axis is

Accepted Answer

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

Question 7

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 8

A force   x in the negative x direction is applied to a particle in the xy plane. The arrow that best represents the torque produced by   x on the particle with respect to the origin is

Accepted Answer

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

Question 9

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 10

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 11

We would like to compare the angular momentum of Mars about its axis of rotation with that of Earth's. The mass of Mars is 11% that of Earth, with a radius 53% that of Earth, and a rotational period 103% that of Earth. Assuming both planets to be uniform spheres calculate the ratio of the angular momentum of Mars to that of Earth.

Accepted Answer

A)  6.0 $\times$ 10-2  
B)  5.7 $\times$ 10-2  
C)  3.2 $\times$ 10-2  
D)  3.0 $\times$10-2  
E)  3.1 $\times$10-2  
A)  6.0 $\times$ 10-2  
B)  5.7 $\times$ 10-2  
C)  3.2 $\times$ 10-2  
D)  3.0 $\times$10-2  
E)  3.1 $\times$10-2

Question 12

A disc with moment of inertia I1 = 40 kg.m2 and angular velocity $\omega$1 = 20 rad/s is dropped on to a stationary second disc along the axis of rotation. The second disc has moment of inertia I2 = 60 kg.m2. How much rotational kinetic energy is lost?

Accepted Answer

A)  3200 J 
B)  4800 J 
C)  8000 J 
D)  11300 J 
E)  15000 J 
A)  3200 J 
B)  4800 J 
C)  8000 J 
D)  11300 J 
E)  15000 J

Question 13

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 14

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 15

A spinning bicycle wheel with a loaded rim (essentially a hoop) is supported by a line at one end of its axle. The radius of the wheel is 0.305 m, and the wheel has a mass of 3.63 kg. It is spinning at 80.0 rad/s, and the center of mass is 15.2 cm from the point of support. The angular velocity of precession is

Accepted Answer

A)  0.0125 rad/s 
B)  0.0318 rad/s 
C)  0.200 rad/s 
D)  0.100 rad/s 
E)  0.625 rad/s 
A)  0.0125 rad/s 
B)  0.0318 rad/s 
C)  0.200 rad/s 
D)  0.100 rad/s 
E)  0.625 rad/s

Question 16

A wheel of moment of inertia 0.136 kg · m2 is spinning with an angular speed of 5000 rad/s. A torque is applied about an axis perpendicular to the spin axis. If the applied torque has a magnitude of 67.8 N · m, the angular velocity of precession will be

Accepted Answer

A)  1.00 rad/s 
B)  0.100 rad/s 
C)  10.0 rad/s 
D)  100 rad/s 
E)  1000 rad/s 
A)  1.00 rad/s 
B)  0.100 rad/s 
C)  10.0 rad/s 
D)  100 rad/s 
E)  1000 rad/s

Question 17

A hoop rotates about an axis through its center with an angular velocity of 40.0 rad/s. If the rotational kinetic energy of the hoop is 400 J, its angular momentum is

Accepted Answer

A)  800 kg · m2/s 
B)  400 kg · m2/s 
C)  200 kg · m2/s 
D)  20 kg · m2/s 
E)  5 kg · m2/s 
A)  800 kg · m2/s 
B)  400 kg · m2/s 
C)  200 kg · m2/s 
D)  20 kg · m2/s 
E)  5 kg · m2/s

Question 18

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 19

The energy-level diagram that most closely represents a rotating molecule with constant moment of inertia is

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5 
A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 20

A gyroscopic wheel spins clockwise as shown. The set of vectors that correctly describes the directions of the torque   , angular momentum   , and angular velocity of precession   p, is

Accepted Answer

A)    (+z);   (-x);   (+y) 
B)    (-z);   (+x);   (-y) 
C)    (+y);   (-x);   (+z) 
D)    (-y);   (-z);   (-x) 
E)    (+y);   (-x);   (-z) 
A)    (+z);   (-x);   (+y) 
B)    (-z);   (+x);   (-y) 
C)    (+y);   (-x);   (+z) 
D)    (-y);   (-z);   (-x) 
E)    (+y);   (-x);   (-z)

A constant torque of 15 N · m acts for 3.0 s on a system of mass 2.0 kg. The change in angular momentum of the system during this period of time is

A woman sits on a spinning piano stool with her arms folded. When she extends her arms, which of the following occurs?

If the distance between two hydrogen atoms of H₂ is 0.1 nm, what is its E_0r?

A particle of mass m is moving with a velocity , in the yz plane as shown. The vector that most nearly represents the angular momentum about the x axis is

A force _x in the negative x direction is applied to a particle in the xy plane. The arrow that best represents the torque produced by _x on the particle with respect to the origin 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

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?

A disc with moment of inertia I₁ = 40 kg.m² and angular velocity $\omega$ ₁ = 20 rad/s is dropped on to a stationary second disc along the axis of rotation. The second disc has moment of inertia I₂ = 60 kg.m². How much rotational kinetic energy is lost?

Spin particles

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

A wheel of moment of inertia 0.136 kg · m² is spinning with an angular speed of 5000 rad/s. A torque is applied about an axis perpendicular to the spin axis. If the applied torque has a magnitude of 67.8 N · m, the angular velocity of precession will be

A hoop rotates about an axis through its center with an angular velocity of 40.0 rad/s. If the rotational kinetic energy of the hoop is 400 J, its angular momentum is

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?

The energy-level diagram that most closely represents a rotating molecule with constant moment of inertia is

A gyroscopic wheel spins clockwise as shown. The set of vectors that correctly describes the directions of the torque , angular momentum , and angular velocity of precession _p, is

Systems of Measurement

Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Rotation

Gravity

Static Equilibrium and Elasticity

Fluids

Oscillations

Wave Motion

Superposition and Standing Waves

Temperature and the Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

The Second Law of Thermodynamics

Thermal Properties and Processes

Filters

Exam 10: Conservation of Angular Momentum

A constant torque of 15 N · m acts for 3.0 s on a system of mass 2.0 kg. The change in angular momentum of the system during this period of time is

A woman sits on a spinning piano stool with her arms folded. When she extends her arms, which of the following occurs?

If the distance between two hydrogen atoms of H2 is 0.1 nm, what is its E0r?

A particle of mass m is moving with a velocity , in the yz plane as shown. The vector that most nearly represents the angular momentum about the x axis is

A force x in the negative x direction is applied to a particle in the xy plane. The arrow that best represents the torque produced by x on the particle with respect to the origin 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

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?

A disc with moment of inertia I1 = 40 kg.m2 and angular velocity ω\omegaω 1 = 20 rad/s is dropped on to a stationary second disc along the axis of rotation. The second disc has moment of inertia I2 = 60 kg.m2. How much rotational kinetic energy is lost?

Spin particles

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

A wheel of moment of inertia 0.136 kg · m2 is spinning with an angular speed of 5000 rad/s. A torque is applied about an axis perpendicular to the spin axis. If the applied torque has a magnitude of 67.8 N · m, the angular velocity of precession will be

A hoop rotates about an axis through its center with an angular velocity of 40.0 rad/s. If the rotational kinetic energy of the hoop is 400 J, its angular momentum is

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?

The energy-level diagram that most closely represents a rotating molecule with constant moment of inertia is

A gyroscopic wheel spins clockwise as shown. The set of vectors that correctly describes the directions of the torque , angular momentum , and angular velocity of precession p, is

Systems of Measurement

Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Rotation

Gravity

Static Equilibrium and Elasticity

Fluids

Oscillations

Wave Motion

Superposition and Standing Waves

Temperature and the Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

The Second Law of Thermodynamics

Thermal Properties and Processes

Filters

If the distance between two hydrogen atoms of H₂ is 0.1 nm, what is its E_0r?

A force _x in the negative x direction is applied to a particle in the xy plane. The arrow that best represents the torque produced by _x on the particle with respect to the origin is

A disc with moment of inertia I₁ = 40 kg.m² and angular velocity $\omega$ ₁ = 20 rad/s is dropped on to a stationary second disc along the axis of rotation. The second disc has moment of inertia I₂ = 60 kg.m². How much rotational kinetic energy is lost?

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

A wheel of moment of inertia 0.136 kg · m² is spinning with an angular speed of 5000 rad/s. A torque is applied about an axis perpendicular to the spin axis. If the applied torque has a magnitude of 67.8 N · m, the angular velocity of precession will be

A gyroscopic wheel spins clockwise as shown. The set of vectors that correctly describes the directions of the torque , angular momentum , and angular velocity of precession _p, is