Question 1

A solid cylinder and a hollow cylinder, each with the same mass $$M$$ and radius $$R$$, are released from rest at the top of an identical incline. Which will reach the bottom first, and why?

Accepted Answer

The solid cylinder, because it has a smaller moment of inertia and more energy is converted to translational motion.

Question 2

Which equation correctly expresses the total kinetic energy of a rolling object (without slipping) with mass $$m$$, center-of-mass velocity $$v_{com}$$, and angular velocity $$\omega$$?

Accepted Answer

$$E_k = \frac{1}{2}mv_{com}^2 + \frac{1}{2}I\$$omega^2$$

Question 3

A force $$F is $$applied tangentially at a distance $$r$$ from the axis of rotation of a disk. What is the magnitude of the torque produced?

Accepted Answer

$$	au = rF\sin	heta$$

Question 4

The moment of inertia for a thin rod of mass $$M$$ and length $$L$$ about an axis through its center perpendicular to its length is:

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 5

A uniform solid sphere and a thin hoop, both with mass $$M$$ and radius $$R$$, roll without slipping down an incline. Which has the greater acceleration and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia relative to its mass.

Question 6

Which of the following best describes the Parallel Axis Theorem?

Accepted Answer

$$I_{parallel} = I_{cm} + Md^2$, where d$ is the distance between axes

Question 7

A block of mass $$2m is $$attached to a string wound around a pulley (disk) of mass $$m$$ and radius $$R. $$The block is released from rest. What is the equation for the net torque on the disk?

Accepted Answer

$$	au_{net} = rF_T$$

Question 8

For a continuous mass distribution, the moment of inertia is calculated using which integral?

Accepted Answer

$$I = \int r^2$ dm$$

Question 9

A non-uniform rod has a mass distribution $$\lambda(x) = B(L^2$ - x^2$). $$Where is the mass density greatest?

Accepted Answer

At $$x = 0$$, the left end of the rod

Question 10

Which condition must be met for an object to roll without slipping?

Accepted Answer

$$v_{com} = r\omega$$

Question 11

A force is applied at an angle $$	heta to a $$lever arm $$r. $$What is the formula for the magnitude of the torque produced?

Accepted Answer

$$	au = rF\sin	heta$$

Question 12

If the net torque on a rotating object is zero, what can be said about its angular acceleration?

Accepted Answer

The angular acceleration is zero.

Question 13

Which of the following is true about the units of the moment of inertia?

Accepted Answer

The units are $$kg \cdot m^2$

Question 14

A disk of mass $$M$$ and radius $$R$$ rotates about an axis through its center. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2}MR^2$

Question 15

A hoop and a solid sphere, both with the same mass and radius, are released from rest at the top of an incline. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia relative to its mass.

Question 16

Which of the following is the correct expression for the rotational kinetic energy of a rotating object?

Accepted Answer

$$E_{k,rot} = \frac{1}{2}I\$$omega^2$$

Question 17

A force $$F is $$applied perpendicular to a door at a distance $$r$$ from the hinges. If the force is doubled, what happens to the torque?

Accepted Answer

The torque doubles.

Question 18

Which of the following statements about the right-hand rule for torque is correct?

Accepted Answer

It determines the direction of the torque vector perpendicular to the plane of rotation.

Question 19

A non-uniform rod has a mass distribution $$\lambda(x) = B(L^2$ - x^2$). $$What is the first step in finding its moment of inertia about the left end?

Accepted Answer

Express $$dm in $$terms of $$dx$$ using the given mass distribution.

Rotational Dynamics and Moment of Inertia: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards