Question 1

Which of the following correctly describes the difference between radial and tangential acceleration for a point on a rotating rigid body?

Accepted Answer

Radial acceleration points toward the axis of rotation and is given by $$ a_r = \$$omega^2$$ r $$, while tangential acceleration is perpendicular to radial acceleration and is given by $$ a_t = \alpha r .$$

Question 2

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

Accepted Answer

$$ \frac{1}{2} I \$$omega^2$$ $$, where $$ I = \frac{1}{2} M R^2$ $$, so $$ K = \frac{1}{4} M R^2$ \$$omega^2$$ $$

Question 3

Which equation correctly relates angular acceleration $$ \alpha  to $$net torque $$ 	au $$ for a rigid body rotating about a fixed axis?

Accepted Answer

$$ 	au = I \alpha $$

Question 4

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 5

A student spins a bicycle wheel and then flips it over. The wheel slows down. Which principle explains this observation?

Accepted Answer

Conservation of angular momentum

Question 6

A figure skater pulls in her arms while spinning. What happens to her angular velocity and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases, conserving angular momentum.

Question 7

A solid sphere and a hollow sphere of equal mass and radius roll down an incline without slipping. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia and thus accelerates faster.

Question 8

Which of the following is the correct expression for the total kinetic energy of a rolling object (without slipping)?

Accepted Answer

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

Question 9

A door of width $$ w  is $$pushed at its edge with a force $$ F $$ perpendicular to the door. What is the torque about the hinge?

Accepted Answer

$$ 	au = F w $$

Question 10

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

$$ m_1$ d_1$ = m_2$ d_2$ $$

Question 11

A rotating platform has a moment of inertia $$ I $$ and angular velocity $$ \omega . If a $$person of mass $$ m $$ steps onto the edge (radius $$ r $$), what is the new angular velocity $$ \omega' $$? Assume no external torque.

Accepted Answer

$$ \omega' = \omega \frac{I}{I + m r^2$} $$

Question 12

Which of the following statements about the parallel axis theorem is correct?

Accepted Answer

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

Question 13

A uniform beam of length $$ L $$ and mass $$ M  is $$supported at its ends. A mass $$ m  is $$hung at a distance $$ x $$ from one end. What is the condition for static equilibrium?

Accepted Answer

The sum of all torques about any point must be zero: $$ \sum 	au = 0 $$

Question 14

A wheel of radius $$ r $$ accelerates from rest with constant angular acceleration $$ \alpha . $$What is the tangential velocity of a point on the rim after time $$ t $$?

Accepted Answer

$$ v = r \alpha t $$

Question 15

A gymnast on a rotating platform changes her body position to increase her moment of inertia. What happens to her rotational kinetic energy, assuming angular momentum is conserved?

Accepted Answer

It decreases because $$ K = \frac{L^2$}{2I} $$ and $$ I $$ increases.

Question 16

A uniform meter stick is pivoted at the 20 cm mark. Where should a 200 g mass be hung to balance the stick horizontally?

Accepted Answer

At the 70 cm mark

Question 17

Which of the following best describes the condition for static equilibrium in a system of particles?

Accepted Answer

The net force and net torque on the system must both be zero.

Question 18

A car rounds a curve of radius $$ r  at $$constant speed $$ v . $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$ a_c = \frac{v^2$}{r} $$

Question 19

A rotating object has angular velocity $$ \omega $$ and angular acceleration $$ \alpha . $$What is the angular displacement $$ 	heta $$ after time $$ t  if it $$starts from rest?

Accepted Answer

$$ 	heta = \frac{1}{2} \alpha t^2$ $$

Physics 5A: Rotational Motion, Dynamics, and Angular Momentum Study Guide

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