AP Physics 1 Unit 6: Energy and Momentum of Rotating Systems

A figure skater spinning with arms extended pulls her arms in. As a result, her angular velocity increases by a factor of 3. By what factor does her rotational kinetic energy change?

A wheel of moment of inertia $I=0.50{\text{kg⋅m}}^2$ has a constant net torque of $2.0\text{N⋅m}$ applied for $4.0\text{s}$ starting from rest. What is its angular momentum at $t=4.0\text{s}$?

A solid sphere ($I=\frac{2}{5}M{R}^2$), a solid disk ($I=\frac{1}{2}M{R}^2$), and a hoop ($I=M{R}^2$) all roll without slipping down the same incline starting from rest. In what order do they reach the bottom?

A sphere rolls without slipping down a frictionless incline. The friction at the contact point does:

Two identical disks (same mass $M$ and radius $R$) start from rest at the top of an incline. Disk A slides down without rotating; Disk B rolls without slipping. Which reaches the bottom with greater speed?

A spinning ice skater has angular momentum $L$ and rotational kinetic energy $KE$. By pulling in his arms, he reduces his moment of inertia by half. What are the new $L$ and $KE$?

A solid disk of moment of inertia $I=0.20{\text{kg⋅m}}^2$ spins at angular speed $\omega =10\text{rad/s}$. What is its rotational kinetic energy?

A child of mass $m$ jumps onto the edge of a stationary merry-go-round (a disk of mass $M$ and radius $R$ on a frictionless bearing) with tangential speed $v$. What is the angular speed of the system after the child lands?