Q: A puck of mass $$3.0\ \mathrm{kg} is $$attached to a cord and revolves in a circle of radius $$2.0\ \mathrm{m}$$ with angular velocity $$5.0\ \mathrm{rad/s}. $$What is its angular momentum?

$$L = 3.0\ \mathrm{kg} \times (2.0\ \mathrm{m})^2$ \times 5.0\ \mathrm{rad/s} = 60\ \mathrm{kg\ m^2$/s}$$

Q: Which equation correctly relates torque and the rate of change of angular momentum?

$$\vec{\tau} = \frac{d\vec{L}}{dt}$$

Question 1

A figure skater is spinning with arms extended. She pulls her arms in close to her body. Which of the following statements best describes what happens to her angular velocity and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases.

Question 2

A puck of mass $$3.0\ \mathrm{kg} is $$attached to a cord and revolves in a circle of radius $$2.0\ \mathrm{m}$$ with angular velocity $$5.0\ \mathrm{rad/s}. $$What is its angular momentum?

Accepted Answer

$$L = 3.0\ \mathrm{kg} 	imes (2.0\ \mathrm{m})^2$ 	imes 5.0\ \mathrm{rad/s} = 60\ \mathrm{kg\ m^2$/s}$$

Question 3

Which of the following best describes the condition for the conservation of angular momentum?

Accepted Answer

The net external torque on the system is zero.

Question 4

A football is thrown in a perfect spiral. Which physical principle explains why the football maintains its orientation in flight?

Accepted Answer

Conservation of angular momentum

Question 5

Two disks are spinning independently on the same axle without friction. Disk 1 has moment of inertia $$I$$ and angular velocity $$\omega ($$clockwise), Disk 2 has $$2I$$ and $$4\omega ($$counterclockwise). They stick together. What is the final angular velocity $$\omega_{net}$$ and its direction?

Accepted Answer

$$\omega_{net} = \frac{7}{3}\omega$$, counterclockwise

Question 6

A gyroscope resists changes to its axis of rotation due to which property?

Accepted Answer

Its high angular momentum

Question 7

Which equation correctly relates torque and the rate of change of angular momentum?

Accepted Answer

$$\vec{	au} = \frac{d\vec{L}}{dt}$$

Question 8

A spinning top precesses because:

Accepted Answer

Gravity exerts a torque perpendicular to the angular momentum.

Question 9

In MRI (Magnetic Resonance Imaging), which physical property of protons is primarily exploited to produce images?

Accepted Answer

Their angular momentum (spin) and precession in a magnetic field

Question 10

A child sits on a spinning merry-go-round. If the child moves closer to the center, what happens to the angular velocity of the merry-go-round (assuming no external torque)?

Accepted Answer

It increases because the moment of inertia decreases.

Question 11

Which of the following is the correct expression for the angular momentum $$L of a $$particle of mass $$m$$ moving with velocity $$v at a $$distance $$r$$ from the axis of rotation?

Accepted Answer

$$L = mrv$$

Question 12

A torque is applied to a stationary wheel, causing it to spin up to angular velocity $$\omega in $$time $$t. If $$the moment of inertia is $$I$$, what is the average torque applied?

Accepted Answer

$$	au = I\frac{\omega}{t}$$

Question 13

Which of the following best explains why a spinning football thrown in a spiral is more stable in flight than a non-spinning one?

Accepted Answer

The spinning football has greater angular momentum, making it resistant to changes in orientation.

Question 14

A spinning ice skater pulls in her arms, reducing her moment of inertia by half. If her initial angular velocity was $$\$$omega_0$$, what is her final angular velocity?

Accepted Answer

$$2\$$omega_0$$

Question 15

Which of the following is NOT a consequence of the conservation of angular momentum?

Accepted Answer

A car accelerates in a straight line.

Question 16

In NMR (Nuclear Magnetic Resonance), what causes the splitting of energy levels for nuclear spins?

Accepted Answer

The presence of an external magnetic field

Question 17

Which of the following equations correctly relates linear and angular momentum for a particle moving in a circle?

Accepted Answer

$$L = r p$$

Question 18

A gyroscope is spinning with angular momentum $$L. A $$torque $$	au is $$applied perpendicular to $$L$$ for a short time $$\Delta t. $$What is the change in angular momentum?

Accepted Answer

$$\Delta L = 	au \Delta t$$

Question 19

Which of the following best describes precession in a gyroscope?

Accepted Answer

A slow change in the orientation of the rotation axis due to an applied torque

Conservation of Angular Momentum and Rotational Dynamics

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