Q: Which of the following is the correct expression for the angular momentum $$\vec{L} of a $$particle with linear momentum $$\vec{p} at $$position $$\vec{r}$$?

$$\vec{L} = \vec{r} \times \vec{p}$$

Q: Which of the following is the correct relationship for the acceleration $$a of a $$rolling object down an incline, compared to a sliding particle?

$$a = \frac{g \sin\theta}{1 + c}$$

Question 1

A solid cylinder (mass $$M$$, radius $$R) $$rolls without slipping down an incline of height $$h. $$What is the speed of its center of mass at the bottom of the incline?

Accepted Answer

$$v = \sqrt{\frac{2gh}{1 + \frac{1}{2}}}$$

Question 2

Which of the following best describes the kinetic energy of a rigid body rolling without slipping?

Accepted Answer

$$K = \frac{1}{2} I_{CM} \$$omega^2$$ + \frac{1}{2} M v_{CM}^2$$

Question 3

A 70 g meter stick is pivoted at one end and released from the horizontal. What principle allows you to calculate the speed of the free end at the lowest point?

Accepted Answer

Conservation of mechanical energy

Question 4

A rolling object moves such that the velocity at the bottom point of contact is:

Accepted Answer

$$v = 0$$

Question 5

Which of the following statements about rolling friction is correct?

Accepted Answer

Rolling friction is always zero for a perfectly rigid body on a perfectly rigid surface.

Question 6

A student sits on a rotating stool holding a spinning bicycle wheel. When the student inverts the wheel, what happens to the student's angular velocity?

Accepted Answer

It changes direction to conserve angular momentum.

Question 7

The torque $$	au$$ produced by a force $$\vec{F}$$ applied at a position vector $$\vec{r}$$ from the axis of rotation is given by:

Accepted Answer

$$	au = rF \sin\phi$$

Question 8

Which of the following is the correct expression for the angular momentum $$\vec{L} of a $$particle with linear momentum $$\vec{p} at $$position $$\vec{r}$$?

Accepted Answer

$$\vec{L} = \vec{r} 	imes \vec{p}$$

Question 9

A solid sphere, a solid cylinder, and a hollow ring are released from rest at the top of an identical incline. Which reaches the bottom first?

Accepted Answer

The solid sphere

Question 10

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

Accepted Answer

Angular momentum

Question 11

The moment of inertia $$I of a $$rigid body depends on:

Accepted Answer

The distribution of mass relative to the axis of rotation

Question 12

Which of the following is the correct rotational analog of Newton's second law?

Accepted Answer

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

Question 13

A wheel of radius $$R$$ rolls without slipping at angular velocity $$\omega. $$What is the speed of the center of mass?

Accepted Answer

$$v_{CM} = \omega R$$

Question 14

Which of the following best describes the direction of the angular velocity vector for a disc rotating anticlockwise in the $$xy-$$plane?

Accepted Answer

Positive $$z-$$direction

Question 15

A toppling chimney often breaks before hitting the ground because:

Accepted Answer

The upper section experiences a tangential acceleration greater than $$g$$ due to shear forces.

Question 16

The parallel axis theorem states that the moment of inertia about any axis parallel to the center of mass axis is:

Accepted Answer

$$I = I_{CM} + MR^2$

Question 17

Which of the following is true for the mechanical energy of a rolling object (without slipping) on a frictionless surface?

Accepted Answer

Mechanical energy is conserved.

Question 18

If a force is applied at an angle $$\phi to $$the position vector $$\vec{r}$$, the magnitude of the torque is maximized when $$\phi is$$:

Accepted Answer

$$90^\circ$$

Question 19

Which of the following is the correct relationship for the acceleration $$a of a $$rolling object down an incline, compared to a sliding particle?

Accepted Answer

$$a = \frac{g \sin	heta}{1 + c}$$

Question 20

Which of the following is NOT a correct property of the cross product?

Accepted Answer

It is commutative: $$\vec{A} 	imes \vec{B} = \vec{B} 	imes \vec{A}$$

Rotation of a Rigid Body and Rotational Dynamics

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