5. Rotation Dynamics

Rotational Energy — Quiz

Test your understanding of rotational energy with 5 practice questions.

Practice Questions

Question 1

A uniform solid disk of mass $M$ and radius $R$ rolls without slipping down an inclined plane of height $h$. What is the speed of the center of mass of the disk at the bottom of the incline, assuming it starts from rest? The moment of inertia of a solid disk about its center is $\frac{1}{2}MR^2$.

Question 2

A uniform rod of mass $M$ and length $L$ is pivoted at its center. A force $F$ is applied perpendicularly to one end of the rod, causing it to rotate. If the rod starts from rest, what is the angular speed after it has rotated through an angle $\theta$? The moment of inertia of a rod pivoted at its center is $\frac{1}{12}ML^2$.

Question 3

A merry-go-round with a moment of inertia $I$ is initially at rest. A child of mass $m$ runs with a speed $v$ tangent to the edge of the merry-go-round at a distance $R$ from the center and jumps on. What is the angular speed of the merry-go-round and child system immediately after the child jumps on?

Question 4

A grinding wheel is rotating at an initial angular speed of $\omega_0$. A constant friction torque $\tau_f$ acts on the wheel, bringing it to rest after an angular displacement of $\Delta\theta$. What is the moment of inertia of the grinding wheel?

Question 5

A solid sphere of mass $M$ and radius $R$ rolls without slipping on a horizontal surface with a translational speed $v$. What is its total kinetic energy? The moment of inertia of a solid sphere about its center is $\frac{2}{5}MR^2$.