Question 1

A solid disk and a hollow ring, both with mass $$m$$ and radius $$R$$, are released from rest at the top of an incline. Which object reaches the bottom first, and why?

Accepted Answer

The solid disk, because it has a smaller moment of inertia and more of its energy goes into translational motion.

Question 2

Which equation correctly expresses the moment of inertia $$I$$ for a point mass $$m at a $$distance $$r$$ from the axis of rotation?

Accepted Answer

$$I = m r^2$

Question 3

A uniform rod of length $$L$$ and mass $$M$$ rotates about an axis through one end perpendicular to its length. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3} M L^2$

Question 4

Which of the following best describes the torque $$	au$$ produced by a force $$F$$ applied at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$	au = r F$$

Question 5

Newton’s Second Law for Rotational Motion is given by which equation?

Accepted Answer

$$\sum 	au = I \alpha$$

Question 6

A solid sphere and a solid cylinder, both with the same mass and radius, roll down the same incline without slipping. Which one has a greater acceleration and why?

Accepted Answer

The solid sphere, because its moment of inertia is smaller relative to its mass.

Question 7

Which equation represents the conservation of mechanical energy for a rolling object (without slipping) down an incline?

Accepted Answer

$$mgh = \frac{1}{2} m v^2$ + \frac{1}{2} I \$$omega^2$$

Question 8

Which of the following is the correct expression for angular momentum $$L of a $$rigid body rotating about a fixed axis?

Accepted Answer

$$L = I \omega$$

Question 9

A satellite orbits Earth in a circular orbit. Which of the following correctly expresses the gravitational force acting on the satellite?

Accepted Answer

$$F = \frac{G M m}{r^2$}$$

Question 10

Which of the following statements about Kepler’s laws is correct?

Accepted Answer

Kepler’s second law states that a planet sweeps out equal areas in equal times.

Question 11

A pendulum of length $$L is $$released from a small angle. What is the period $$T of $$its oscillation?

Accepted Answer

$$T = 2 \pi \sqrt{\frac{L}{g}}$$

Question 12

Which of the following best describes simple harmonic motion (SHM)?

Accepted Answer

Motion where the restoring force is proportional to displacement and directed toward equilibrium.

Question 13

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with angular frequency $$\omega. $$Which equation is correct?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 14

A block attached to a spring oscillates with amplitude $$A. $$What is its maximum speed $$v_{max}$$?

Accepted Answer

$$v_{max} = \omega A$$

Question 15

Which of the following is true for the energy in a simple harmonic oscillator?

Accepted Answer

Total mechanical energy is constant and equals $$\frac{1}{2} k A^2$.

Question 16

A child swings on a playground swing (a simple pendulum). If the child increases the amplitude of the swing, what happens to the period?

Accepted Answer

The period remains nearly the same for small amplitudes.

Question 17

A rotating object has angular velocity $$\omega$$ and moment of inertia $$I. If no $$external torque acts, what happens to its angular momentum?

Accepted Answer

Angular momentum remains constant.

Question 18

A mass $$m is $$attached to a spring and oscillates with period $$T. If $$the mass is doubled, what happens to the period?

Accepted Answer

The period increases by a factor of $$\sqrt{2}.$$

Question 19

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

Accepted Answer

$$I = \frac{2}{5} M R^2$

Review Notes: Rotation of a Rigid Body, Gravity, and Oscillations (PHY 2111 Exam 4)

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