Question 1

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. What is the period $$T of $$the oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 2

Which of the following best describes the restoring force $$F in $$simple harmonic motion for a spring?

Accepted Answer

$$F = -kx$$

Question 3

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

Accepted Answer

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

Question 4

A rotating disk has a moment of inertia $$I$$ and angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2}I\$$omega^2$$

Question 5

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

Accepted Answer

$$	au = rF\sin	heta$$

Question 6

A child spins a wheel with moment of inertia $$I at $$angular velocity $$\omega. If no $$external torque acts, what physical law explains why $$I\omega$$ remains constant?

Accepted Answer

Conservation of Angular Momentum

Question 7

A gymnast on a rotating platform pulls her arms in, reducing her moment of inertia from $$I_1 to$$ $$I_2. If $$her initial angular velocity is $$\$$omega_1$$, what is her final angular velocity $$\$$omega_2$$?

Accepted Answer

$$\$$omega_2$$ = \frac{I_1$}{I_2$}\$$omega_1$$

Question 8

Which of the following is NOT a necessary condition for an object to be in rotational equilibrium?

Accepted Answer

The angular velocity must be zero.

Question 9

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

Accepted Answer

$$I = \frac{1}{3}ML^2$

Question 10

A wheel is spinning with angular velocity $$\omega$$ and a constant frictional torque $$	au_f$$ acts to slow it down. What is the time $$t it $$takes to stop if its moment of inertia is $$I$$?

Accepted Answer

$$t = \frac{I\omega}{	au_f}$$

Question 11

A satellite orbits Earth in a circular path. Which force provides the necessary centripetal acceleration?

Accepted Answer

Gravitational force

Question 12

A car rounds a curve of radius $$r at $$speed $$v. $$What is the minimum coefficient of friction $$\mu$$ required to prevent slipping?

Accepted Answer

$$\mu = \frac{v^2$}{rg}$$

Question 13

A spinning ice skater pulls in her arms, decreasing her moment of inertia. What happens to her rotational kinetic energy, assuming angular momentum is conserved?

Accepted Answer

It increases

Question 14

Which of the following statements about Newton's Second Law for rotation is correct?

Accepted Answer

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

Question 15

A solid sphere and a hollow sphere of equal mass and radius roll down an incline. Which reaches the bottom first and why?

Accepted Answer

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

Question 16

A force $$F is $$applied tangentially to a wheel of radius $$r$$ for time $$t. $$What is the change in angular momentum $$\Delta L$$?

Accepted Answer

$$\Delta L = Frt$$

Question 17

A rotating object has angular velocity $$\omega$$ and is subject to a net torque $$	au. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{	au}{I}$$

Question 18

A seesaw is balanced with a child of mass $$m_1$$ sitting at distance $$d_1$$ from the pivot and another child of mass $$m_2 at $$distance $$d_2 on $$the other side. What is the condition for equilibrium?

Accepted Answer

$$m_1d_1 = m_2d_2$$

Question 19

Which of the following is true about the parallel axis theorem?

Accepted Answer

It allows calculation of the moment of inertia about any axis parallel to one through the center of mass.

Question 20

A flywheel stores energy by rotating. If its moment of inertia is doubled but its angular velocity is halved, what happens to its rotational kinetic energy?

Accepted Answer

It is halved

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

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