Q: The vector cross product $$\vec{A} \times \vec{B}$$ has a magnitude given by which formula?

$$|\vec{A} \times \vec{B}| = AB \sin \theta$$

Q: Which formula correctly relates torque $$\vec{\tau}$$ and the rate of change of angular momentum $$\vec{L}$$?

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

Question 1

A solid sphere, a solid disk, and a hoop all start from rest and roll down the same incline without slipping. Ignoring friction losses and assuming equal mass and radius, which object reaches the bottom first?

Accepted Answer

The sphere

Question 2

Which of the following is the correct expression for the moment of inertia of a solid sphere of mass $$M$$ and radius $$R$$ about an axis through its center?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 3

The vector cross product $$\vec{A} 	imes \vec{B}$$ has a magnitude given by which formula?

Accepted Answer

$$|\vec{A} 	imes \vec{B}| = AB \sin 	heta$$

Question 4

A particle of mass $$m$$ moves in a circle of radius $$r at $$speed $$v in a $$counterclockwise direction. What is the magnitude of its angular momentum about the center?

Accepted Answer

$$L = mvr$$

Question 5

Which statement best describes the conservation of angular momentum?

Accepted Answer

Angular momentum is conserved only if the net external torque is zero.

Question 6

A spinning top precesses around its point of contact due to gravity. Which equation gives the angular velocity of precession $$\omega_p$$?

Accepted Answer

$$\omega_p = \frac{Mgr}{I \omega}$$

Question 7

Which of the following best describes the direction of the torque vector $$\vec{	au}$$ produced by a force $$\vec{F}$$ applied at position $$\vec{r}$$ from the axis?

Accepted Answer

It is perpendicular to both $$\vec{r}$$ and $$\vec{F}$$

Question 8

A person is holding a spinning bicycle wheel by its axle. If the person tilts the axle upward, in which direction does the wheel begin to rotate due to the torque applied?

Accepted Answer

To the left

Question 9

Which of the following is true about the angular momentum of a system of particles?

Accepted Answer

It can change only if there is an external torque acting on the system.

Question 10

Which formula correctly relates torque $$\vec{	au}$$ and the rate of change of angular momentum $$\vec{L}$$?

Accepted Answer

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

Question 11

In the Southern Hemisphere, hurricanes rotate in which direction due to the Coriolis effect?

Accepted Answer

Clockwise

Question 12

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

Accepted Answer

The increase in mass of a rotating object

Question 13

A rigid object rotates about a fixed axis with angular velocity $$\omega. $$What is its angular momentum $$L$$?

Accepted Answer

$$L = I \omega$$

Question 14

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

Accepted Answer

The system's angular momentum changes over time.

Question 15

A hoop, disk, and sphere of equal mass and radius roll down an incline. Which has the largest moment of inertia?

Accepted Answer

The hoop

Question 16

Which physical phenomenon is explained by the Coriolis effect?

Accepted Answer

The rotation of hurricanes

Question 17

Which of the following is a correct statement about inertial and non-inertial frames of reference?

Accepted Answer

Newton's laws hold only in inertial frames.

Question 18

A force $$\vec{F} is $$applied at a distance $$r$$ from the axis of rotation. What is the torque produced?

Accepted Answer

$$	au = rF \sin 	heta$$

Question 19

Which of the following best describes the right-hand rule for the direction of the cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

Point your fingers in the direction of $$\vec{A}$$, curl them toward $$\vec{B}$$, and your thumb points in the direction of the cross product.

Question 20

Which of the following is a real-world application of angular momentum conservation?

Accepted Answer

A figure skater spinning faster by pulling in her arms

Angular Momentum and Its Applications

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