A rotor starts at $\omega_0=2.00\text{ rad/s}$ and accelerates uniformly at $\alpha=1.50\text{ rad/s}^2$ for $4.00\text{ s}$. Determine its final angular velocity and angular displacement.

A disk of radius $0.600\text{ m}$ rotates at $5.00\text{ rad/s}$. Determine the tangential speed and centripetal acceleration of a point on its rim.

Two point masses, $3.00\text{ kg}$ at $2.00\text{ m}$ and $5.00\text{ kg}$ at $4.00\text{ m}$ from an axis, rotate together. Determine the system moment of inertia.

A uniform solid sphere has $M=10.0\text{ kg}$ and $R=0.500\text{ m}$. Determine its moment of inertia about an axis tangent to the sphere and parallel to a centroidal diameter.

A $0.300\text{ m}$ wrench is pulled with a $50.0\text{ N}$ force at $60.0^\circ$ to the handle. Determine the torque magnitude about the bolt.

Enlarge

A $2.00\text{ kg}$ block hangs from a massless string wrapped around a freely rotating solid cylindrical pulley of mass $6.00\text{ kg}$ and radius $0.300\text{ m}$. The string does not slip. Determine the block acceleration using $g=9.80\text{ m/s}^2$.

Enlarge

A flywheel has moment of inertia $I=18.0\text{ kg}\cdot\text{m}^2$ and rotates at $12.0\text{ rad/s}$. Determine its rotational kinetic energy.

A $10.0\text{ kg}$ solid cylinder of radius $0.500\text{ m}$ rolls without slipping at $4.00\text{ m/s}$. Determine its translational, rotational, and total kinetic energies.

A skater has $I_i=2.40\text{ kg}\cdot\text{m}^2$ and $\omega_i=3.00\text{ rad/s}$. She changes configuration to $I_f=0.800\text{ kg}\cdot\text{m}^2$ with negligible external torque. Determine $\omega_f$.

A stationary merry-go-round has $I=500\text{ kg}\cdot\text{m}^2$ and radius $2.00\text{ m}$. A $40.0\text{ kg}$ child running tangentially at $5.00\text{ m/s}$ jumps onto its rim. Determine the common angular velocity.

Disk 1 has $I_1=0.040\text{ kg}\cdot\text{m}^2$ and rotates at $40.0\text{ rad/s}$ while Disk 2 has $I_2=0.060\text{ kg}\cdot\text{m}^2$ and is initially at rest. They are brought into contact and reach a common angular speed. Determine the final speed and percentage of rotational kinetic energy dissipated.