Practice Problems

1. A solid cylinder of mass 4 kg and radius 0.25 m rolls without slipping at 2 m/s. Find its translational, rotational, and total kinetic energy.
2. A uniform rod 1.5 m long and 3 kg is pivoted at one end. Calculate the torque due to its weight when horizontal.
3. A disc of moment of inertia 2 kg·m² rotates at 10 rad/s. Find its angular momentum and rotational kinetic energy.
4. A wheel of mass 5 kg and radius 0.4 m rolls down a 2 m high incline without slipping. Determine its speed at the bottom.
5. A solid sphere of mass 2 kg and radius 0.2 m rotates at 15 rad/s. Find its rotational kinetic energy.
6. A uniform beam of length 3 m and mass 6 kg is supported at its midpoint. A 50 N weight is hung 1 m from the support. Calculate the net torque about the midpoint.
7. A cylinder of radius 0.3 m rolls down an incline of height 1.5 m. Determine the linear speed at the bottom.
8. A rotating disc has an angular momentum of 18 kg·m²/s and a moment of inertia of 3 kg·m². Find its angular velocity.
9. A solid cylinder rolls without slipping at 5 m/s. Find its translational and rotational kinetic energy if its mass is 8 kg and radius 0.2 m.
10. A uniform rod 2 m long and mass 4 kg is pivoted at one end. A force of 20 N is applied perpendicular at the free end. Calculate the torque.