Q: A particle of mass $$m$$ moves with velocity $$\vec{v} at a $$position $$\vec{r}$$ relative to the origin. What is the expression for its angular momentum $$\vec{L}$$ about the origin?

$$\vec{L} = \vec{r} \times m \vec{v}$$

Q: Which of the following best describes the relationship between torque $$\vec{\tau}$$, position vector $$\vec{r}$$, and force $$\vec{F}$$?

$$\vec{\tau} = \vec{r} \times \vec{F}$$

Question 1

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

Accepted Answer

Her angular velocity increases because her moment of inertia decreases, conserving angular momentum.

Question 2

Which of the following equations correctly relates torque $$	au to $$angular acceleration $$\alpha$$ for a rigid body rotating about a fixed axis?

Accepted Answer

$$	au = I \alpha$$

Question 3

A neutron star forms from the collapse of a massive star. If the original star has a radius $$R_i$$ and rotates with period $$T_i$$, and the neutron star has radius $$R_f$$ and period $$T_f$$, which equation correctly relates the initial and final periods, assuming angular momentum is conserved?

Accepted Answer

$$T_f = T_i \left( \dfrac{R_f}{R_i} \$$right)^2$$

Question 4

Which of the following statements about the direction of angular velocity $$\vec{\omega} is $$correct?

Accepted Answer

The direction of $$\vec{\omega} is $$along the axis of rotation, determined by the right-hand rule.

Question 5

A solid sphere of mass $$M$$ and radius $$R$$ rotates about an axis through its center with angular velocity $$\omega. $$What is its angular momentum?

Accepted Answer

$$L = \dfrac{2}{5} M R^2$ \omega$$

Question 6

A particle of mass $$m$$ moves with velocity $$\vec{v} at a $$position $$\vec{r}$$ relative to the origin. What is the expression for its angular momentum $$\vec{L}$$ about the origin?

Accepted Answer

$$\vec{L} = \vec{r} 	imes m \vec{v}$$

Question 7

Which of the following is NOT a conserved quantity in classical physics?

Accepted Answer

Temperature

Question 8

A disk is spinning freely in space with no external torques acting on it. If its moment of inertia suddenly doubles (e.g., by mass redistribution), what happens to its angular velocity?

Accepted Answer

It is halved.

Question 9

Which of the following best describes the relationship between torque $$\vec{	au}$$, position vector $$\vec{r}$$, and force $$\vec{F}$$?

Accepted Answer

$$\vec{	au} = \vec{r} 	imes \vec{F}$$

Question 10

A wheel is spinning with angular velocity $$\omega$$ and is slowing down due to friction. What is the direction of its angular acceleration $$\vec{\alpha}$$?

Accepted Answer

Opposite to the direction of $$\vec{\omega}$$

Question 11

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

Accepted Answer

Angular momentum remains constant; angular velocity increases.

Question 12

Which of the following is the rotational analog of Newton's second law $$F = ma$$?

Accepted Answer

$$	au_{net} = I \alpha$$

Question 13

A star with mass $$M$$ and initial radius $$R_i$$ collapses to a neutron star with radius $$R_f. If $$the initial angular velocity is $$\omega_i$$, what is the final angular velocity $$\omega_f ($$assuming the star is a uniform sphere and angular momentum is conserved)?

Accepted Answer

$$\omega_f = \omega_i \left( \dfrac{R_i}{R_f} \$$right)^2$$

Question 14

Which of the following best describes the cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

A vector perpendicular to the plane defined by $$\vec{A}$$ and $$\vec{B}$$, with magnitude $$|\vec{A}||\vec{B}|\sin	heta$$

Question 15

If the net external torque on a system is zero, which of the following statements is true?

Accepted Answer

The total angular momentum of the system is conserved.

Question 16

A rotating object has angular momentum $$L = I \omega. If $$the moment of inertia $$I is $$tripled while keeping $$L$$ constant, what happens to $$\omega$$?

Accepted Answer

$$\omega$$ becomes one-third its original value.

Question 17

Which of the following is the correct analogy between translational and rotational motion?

Accepted Answer

Linear momentum $$p = m v$$ corresponds to angular momentum $$L = I \omega$$

Question 18

A force $$\vec{F} is $$applied at a point whose position vector relative to the axis of rotation is $$\vec{r}. If$$ $$\vec{F} is $$parallel to $$\vec{r}$$, what is the torque about the axis?

Accepted Answer

Zero

Question 19

A spinning star contracts to a smaller radius. Which of the following best explains why its rotation rate increases?

Accepted Answer

Its moment of inertia decreases, so angular velocity increases to conserve angular momentum.

Conservation of Angular Momentum and Rotational Dynamics

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