Question 1

A potter's wheel (assuming a uniform disk of mass 5.0 kg and diameter 0.50 m) rotates around a vertical axis through its center at a frequency of 10 rad/s. The potter throws a 4.0-kg chunk of clay, shaped as a flat disk of radius 6.0 cm, onto the center of the rotating wheel. The frequency of rotation of the wheel after the clay sticks to it is
A) 8.4 rad/s.
B) 9.6 rad/s.
C) 10 rad/s.
D) 12 rad/s.
E) 19 rad/s.

Accepted Answer

The conservation of angular momentum applies here. The initial angular momentum of the system is the angular momentum of the wheel alone, which is I_w * ω_i, where I_w is the moment of inertia of the wheel and ω_i is the initial angular velocity. The moment of inertia of the wheel is (1/2) * m_w * r_w^2. After the clay sticks, the total moment of inertia is I_w + I_c, where I_c is the moment of inertia of the clay, (1/2) * m_c * r_c^2. The final angular velocity ω_f is found using L_initial = L_final, or I_w * ω_i = (I_w + I_c) * ω_f. Solving for ω_f gives approximately 9.6 rad/s.

Question 2

The protons and neutrons making up a nucleus are suddenly rearranging themselves so that the nucleus' moment of inertia decreases by a factor of 4. The change in the rotational kinetic energy during this process is
A) zero.
B) 2 times the initial kinetic energy of rotation.
C) 3 times the initial kinetic energy of rotation.
D) 4 times the initial kinetic energy of rotation.
E) 16 times the initial kinetic energy of rotation.

Accepted Answer

The rotational kinetic energy is inversely proportional to the moment of inertia. If the moment of inertia decreases by a factor of 4, the rotational kinetic energy increases by a factor of 4. The change in energy is then 3 times the initial energy.

Question 3

A diver can reduce her moment of inertia by a factor of about 3.14 when changing from the straight position to the tuck position. If she makes 3.0 rotations in 2.0 s when in the tuck position, her angular speed when in the straight position is
A) 0.48 rad/s.
B) 0.52 rad/s.
C) 3.0 rad/s.
D) 4.7 rad/s.
E) 30 rad/s.

Accepted Answer

The answer of A diver can reduce her moment of...

Question 4

The mean orbital speed of Mars is 0.80 times that of the Earth in their orbits around the Sun. Because the mean orbital radius of Mars is 1.52 times that of the Earth, and the mass of Mars is 0.11 times that of the Earth, the ratio of the angular momentum of Mars to that of the Earth in their orbits around the Sun is
A) 99.
B) 26.
C) 0.26.
D) 0.21.
E) 0.13.

Accepted Answer

The answer of The mean orbital speed of Mars is...

Question 5

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a mass in each outstretched hand. When you suddenly release and drop the masses, your angular velocity
A) increases.
B) stays the same.
C) decreases.
D) becomes zero.

Accepted Answer

When you release the masses, the external torque acting on the system (you and the stool) is zero. According to the conservation of angular momentum, if no external torque is applied, the angular momentum of a system remains constant. Since angular momentum is the product of moment of inertia and angular velocity, and your moment of inertia decreases when you release the masses (as they are no longer part of the system), one might expect your angular velocity to change to conserve angular momentum. However, the question specifies that the masses are dropped, not thrown, meaning they do not impart any additional angular momentum to the system upon release. Therefore, your angular velocity remains unchanged.

Question 6

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180^o), you will A) rotate in the same direction the bicycle wheel was originally rotating. B) stay still. C) rotate in the direction opposite to that of the bicycle wheel's original rotation.

Accepted Answer

The angular momentum of the system (you and the wheel) is conserved. When you flip the wheel, its angular momentum changes sign. To conserve angular momentum, you must rotate in the opposite direction.

Question 7

A uniform thin rod of length 0.40 m and mass 4.0 kg can rotate in the horizontal plane about a vertical axis through one end. The rod is at rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into the free end of the rod. As viewed from above, the direction of the bullet's velocity makes an angle of 60^o with the rod. The bullet lodges in the rod, and the angular velocity of the rod is 10 rad/s immediately after collision. The magnitude of the bullet's velocity just before impact was A) 2.1 $\times$ 10² m/s. B) 1.8 $\times$ 10³ m/s. C) 3.6 $\times$ 10³ m/s. D) 1.8 $\times$ 10⁴ m/s. E) 2.1 $\times$ 10⁴ m/s.

Accepted Answer

The answer of A uniform thin rod of length 0.40...

Question 8

A top is spinning rapidly on a table, its axis inclined to the vertical. As the spin of the top gradually decreases, the precession frequency of the top
A) increases.
B) decreases.
C) remains unchanged.
D) is unknown; more information is needed to work out the answer.

Accepted Answer

As the spin of the top decreases, its angular momentum decreases, causing the precession frequency to increase to conserve angular momentum.

Question 9

A top is spinning rapidly on a table, its axis inclined to the vertical. If only the angle of inclination is changed, each of the following quantities changes except the
A) torque.
B) precession frequency.
C) angular momentum.
D) precessional angular velocity.

Accepted Answer

The answer of A top is spinning rapidly on a...

Question 10

A girl carries a box that contains a gyroscope (a flywheel suspended in gimbals) that spins around the east-west axis. The girl is walking in the same direction as the rotational axis of the gyroscope, then suddenly turns to the left. The front part of the box

A) moves upward.
B) moves downward.
C) does not change its position.
D) rotates north.
E) rotates south.

Accepted Answer

The answer of A girl carries a box that contains...

Question 11

A thin, 1.00-m-long rod of mass 1.00 kg has a solid sphere of radius 0.25 m and mass 0.50 kg attached to one end. The arrangement is originally vertical and stationary, with the sphere at the top. The system is free to pivot about the bottom end of the rod after being given a slight nudge. The speed of the sphere after the system rotates through 90^o is A) 1.10 m/s. B) 1.22 m/s. C) 1.80 m/s. D) 3.14 m/s. E) 5.53 m/s.

Accepted Answer

The answer of A thin, 1.00-m-long rod of mass 1.00...

Quiz 13: Dynamics of a Rigid Body

The protons and neutrons making up a nucleus are suddenly rearranging themselves so that the nucleus' moment of inertia decreases by a factor of 4. The change in the rotational kinetic energy during this process is

A diver can reduce her moment of inertia by a factor of about 3.14 when changing from the straight position to the tuck position. If she makes 3.0 rotations in 2.0 s when in the tuck position, her angular speed when in the straight position is

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a mass in each outstretched hand. When you suddenly release and drop the masses, your angular velocity

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180^o) , you will

A top is spinning rapidly on a table, its axis inclined to the vertical. As the spin of the top gradually decreases, the precession frequency of the top

A top is spinning rapidly on a table, its axis inclined to the vertical. If only the angle of inclination is changed, each of the following quantities changes except the

A girl carries a box that contains a gyroscope (a flywheel suspended in gimbals) that spins around the east-west axis. The girl is walking in the same direction as the rotational axis of the gyroscope, then suddenly turns to the left. The front part of the box

Quiz 13: Dynamics of a Rigid Body

The protons and neutrons making up a nucleus are suddenly rearranging themselves so that the nucleus' moment of inertia decreases by a factor of 4. The change in the rotational kinetic energy during this process is

A diver can reduce her moment of inertia by a factor of about 3.14 when changing from the straight position to the tuck position. If she makes 3.0 rotations in 2.0 s when in the tuck position, her angular speed when in the straight position is

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a mass in each outstretched hand. When you suddenly release and drop the masses, your angular velocity

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180o) , you will

A top is spinning rapidly on a table, its axis inclined to the vertical. As the spin of the top gradually decreases, the precession frequency of the top

A top is spinning rapidly on a table, its axis inclined to the vertical. If only the angle of inclination is changed, each of the following quantities changes except the

A girl carries a box that contains a gyroscope (a flywheel suspended in gimbals) that spins around the east-west axis. The girl is walking in the same direction as the rotational axis of the gyroscope, then suddenly turns to the left. The front part of the box

You are sitting on a stool that can rotate friction-free about its vertical axis, holding a spinning bicycle wheel that rotates in a horizontal plane. When you flip the bicycle wheel (turn it over through 180^o) , you will