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 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 wheel of radius 0.5 m is rolling without slipping. If the angular velocity of the wheel is 6 rad/s, what is the linear velocity of its center of mass?

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

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