AP Physics C: Mechanics Unit 5: Rotation

A net torque ${\tau }_{net}=10$ N·m acts on a solid sphere ($I=\frac{2}{5}M{R}^2$, $M=5$ kg, $R=0.2$ m). Find $\alpha$.

A student derives the moment of inertia of a thin spherical shell of mass $M$ and radius $R$ about a diameter. Which result is correct?

A uniform rod ($M$, $L$) is held horizontal, pivoted at one end, and released. Using $\tau =I\alpha$ and torque from gravity, find the initial angular acceleration and the linear acceleration of the free end.

A wheel starts from rest and reaches an angular velocity of $10$ rad/s in $5$ s under constant angular acceleration. What is the angular acceleration?

A uniform solid disk of mass $M$ and radius $R$ has moment of inertia about its central axis $I=\frac{1}{2}M{R}^2$. A net torque $\tau =4$ N·m is applied to a disk with $M=2$ kg and $R=1$ m. What is the angular acceleration?

A figure skater with $I_1=4$ kg·m² spins at $2$ rad/s and pulls in arms to reach $I_2=1$ kg·m². What is the new angular velocity?

A particle of mass $m=0.5$ kg moves in a circle of radius $r=2$ m at speed $v=4$ m/s. What is its angular momentum about the center?

A solid cylinder ($I=\frac{1}{2}M{R}^2$) rolls without slipping down a frictionless incline of height $h$. Using energy conservation, find the speed at the bottom.

A torque $\tau (t)=3t$ N·m acts on a flywheel with $I=6$ kg·m² starting from rest. Find $\omega$ at $t=4$ s.

Using the integral definition $I=\int r^{2}dm$, find the moment of inertia of a thin uniform rod of mass $M$ and length $L$ about one end.

A disk ($I_1=2$ kg·m², ${\omega }_1=6$ rad/s) drops onto a stationary disk ($I_2=3$ kg·m²) on the same frictionless axle. They reach a common angular velocity ${\omega }_f$. How much kinetic energy is lost?

A uniform disk ($I_{cm}=\frac{1}{2}M{R}^2$) has a small bolt of mass $m$ attached at its rim. Using the parallel-axis theorem, what is the total moment of inertia about the disk's center?