Rotating Systems: Energy & Momentum

A solid cylinder with mass $M$ and radius $R$ is rotating at an angular velocity $\omega$. What is its rotational kinetic energy?

A disk has a rotational inertia of $I = 4 , kg \cdot m^2$ and is rotating with an angular velocity of $\omega = 3 , rad/s$. What is its rotational kinetic energy?

A wheel with a mass of $2 , kg$ and a radius of $0.5 , m$ rolls down an incline without slipping. At a certain point, its center of mass is moving at $3 , m/s$. Assuming the wheel is a solid disk, calculate its total kinetic energy at that point.

A sphere rolls without slipping. What percentage of its total kinetic energy is rotational?

A yo-yo is released from rest. Find its speed at the bottom using conservation of energy.

A sphere rolls down a ramp and compresses a spring. Find the compression of the spring.

A ball rolls down a hill. What is the primary difference between its rotational and translational kinetic energy?

A cylinder rolls down an incline. Find its final velocity using conservation of energy.

Two disks are rotating in opposite directions. Disk A has a rotational kinetic energy of 20 J and Disk B has a rotational kinetic energy of 30 J. How does the total rotational kinetic energy change when they are combined?

Two flywheels with known rotational kinetic energies are connected. Flywheel 1 has a rotational kinetic energy of $K_1 = 50 , J$ and Flywheel 2 has a rotational kinetic energy of $K_2 = 75 , J$. What is the total rotational kinetic energy of the system?