Rotating Systems: Energy & Momentum

Which of the following best describes rotational kinetic energy?

A spinning top has a rotational inertia of $2 \text{ kg m}^2$ and an angular velocity of $5 \text{ rad/s}$. What is its rotational kinetic energy?

A solid sphere with a mass of $5 \text{ kg}$ and a radius of $0.2 \text{ m}$ is rotating at $10 \text{ rad/s}$. Given that the moment of inertia of a solid sphere is $I = \frac{2}{5}MR^2$, what is its rotational kinetic energy?

A wheel with a moment of inertia of $2.0 \text{ kg m}^2$ and a radius of $0.5 \text{ m}$ is rolling without slipping at a linear speed of $10 \text{ m/s}$. What is its total kinetic energy?

A solid cylinder with mass $M$ and radius $R$ rolls down an incline of height $h$ without slipping. What is its speed at the bottom of the incline?

A motor applies a constant torque of $10 \text{ Nm}$ to a flywheel with a moment of inertia of $2 \text{ kg m}^2$. If the flywheel starts from rest, what is its rotational kinetic energy after 5 seconds?

A skater spins with her arms extended. When she pulls her arms in, her moment of inertia decreases. How does her rotational kinetic energy change, assuming no external torques?

Rotational kinetic energy is a scalar quantity. What does this imply for calculations involving rotational kinetic energy?

Which of the following is a common mistake to avoid when calculating rotational kinetic energy?

What happens to the rotational kinetic energy of an object if its angular velocity is doubled, assuming the moment of inertia remains constant?