Question 1

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. If the amplitude of oscillation is doubled, what happens to the maximum kinetic energy of the mass?

Accepted Answer

It is quadrupled.

Question 2

A simple pendulum of length $$L$$ and mass $$m is $$released from a small angle. Which of the following correctly gives the period $$T of $$the pendulum for small oscillations?

Accepted Answer

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

Question 3

A block attached to a horizontal spring oscillates with simple harmonic motion. At what position is the acceleration of the block maximum?

Accepted Answer

At the maximum displacement (amplitude).

Question 4

A uniform rod of length $$L$$ and mass $$M is $$pivoted at one end and swings as a physical pendulum. What is the correct expression for its period for small oscillations?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{2L}{3g}}$$

Question 5

A force $$F is $$applied tangentially to a disk of radius $$R$$ and mass $$M$$ that is free to rotate about its center. What is the resulting angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \dfrac{F R}{\dfrac{1}{2} M R^2$}$$

Question 6

A solid sphere and a hollow cylinder, both of equal mass and radius, are released from rest at the top of an incline. Which one reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia.

Question 7

A figure skater pulls in her arms during a spin, reducing her moment of inertia to half its original value. If her initial angular velocity was $$\$$omega_0$$, what is her final angular velocity?

Accepted Answer

$$2\$$omega_0$$

Question 8

A wheel of radius $$R is $$rolling without slipping at speed $$v. $$What is the angular velocity $$\omega of $$the wheel?

Accepted Answer

$$\omega = \dfrac{v}{R}$$

Question 9

A uniform disk of mass $$M$$ and radius $$R$$ rotates about its center with angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \dfrac{1}{2} \left(\dfrac{1}{2} M R^2$\right) \$$omega^2$$

Question 10

A satellite orbits Earth in a circular orbit. Which of the following statements about its angular momentum is correct (neglecting air resistance)?

Accepted Answer

Its angular momentum remains constant.

Question 11

A rod of length $$L$$ and mass $$M is $$rotating about its center with angular velocity $$\omega. $$What is its moment of inertia?

Accepted Answer

$$I = \dfrac{1}{12} M L^2$

Question 12

A force $$F is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$	heta$$ with the lever arm. What is the torque $$	au$$ produced?

Accepted Answer

$$	au = F r \sin 	heta$$

Question 13

A child sits on a merry-go-round at a distance $$R$$ from the center. If the merry-go-round rotates with angular velocity $$\omega$$, what is the child's linear speed $$v$$?

Accepted Answer

$$v = \omega R$$

Question 14

A solid sphere of mass $$M$$ and radius $$R is $$rolling without slipping down an incline. What fraction of its total kinetic energy is rotational?

Accepted Answer

$$\dfrac{2}{7}$$

Question 15

A uniform rod of length $$L is $$pivoted at one end and held horizontally. What is the torque due to gravity about the pivot?

Accepted Answer

$$	au = \dfrac{1}{2} M g L$$

Question 16

A spinning neutron star (pulsar) slows down over time due to emission of electromagnetic radiation. Which conservation law explains the decrease in angular velocity?

Accepted Answer

Conservation of angular momentum.

Question 17

A gymnast on a high bar tucks her body to spin faster. Which physical quantity is conserved during this maneuver?

Accepted Answer

Angular momentum.

Question 18

A flywheel is spinning with angular velocity $$\omega$$ and has a moment of inertia $$I. If a $$constant torque $$	au is $$applied in the opposite direction, how long does it take to bring the flywheel to rest?

Accepted Answer

$$t = \dfrac{I \omega}{	au}$$

Question 19

A car makes a sharp turn to the left. Which direction does the friction force on the tires point?

Accepted Answer

To the left.

Question 20

A spinning ice skater extends her arms outward. What happens to her rotational kinetic energy, assuming no external torques act?

Accepted Answer

It decreases.

Study Guide: Oscillations, Rotational Motion, and Conservation Laws (PHYS-140)

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