Rotating Systems: Energy & Momentum

A bicycle wheel is rolling along the ground without slipping. What is the relationship between the linear velocity ($v_{cm}$) of the wheel's center of mass and its angular velocity ($\omega$)?

A bowling ball rolls down a lane without slipping. Which of the following best describes its total kinetic energy ($K_{tot}$)?

A wheel with a radius of 0.2 meters starts from rest and rolls without slipping down a ramp. If its angular acceleration is 5 rad/s², what is the linear acceleration of the center of mass of the wheel?

A solid sphere is rolling horizontally without slipping. In what direction does the force of static friction act on the sphere?

A wheel is rolling and slipping simultaneously on a road. What effect does kinetic friction have on the wheel's total kinetic energy?

A solid sphere with a mass of 2 kg and a radius of 0.1 m is rolling on a flat surface with a linear velocity of 3 m/s and an angular velocity of 30 rad/s. What is its total kinetic energy?

A solid cylinder rolls without slipping down an inclined plane. What is the relationship between its linear acceleration ($a_{cm}$) and angular acceleration ($\alpha$)?

A ball is rolling on a level surface without slipping. What type of friction is acting at the point of contact between the ball and the surface, and does this friction do work on the ball?

A car's wheels are spinning as it attempts to accelerate on an icy road. In this situation, what is true about the relationship between the linear and rotational motion of the wheels?

A solid cylinder and a hollow cylinder, both with the same mass and radius, are released from rest at the top of an incline. Assuming they roll without slipping, which one will reach the bottom first?