10.4 Moment of Inertia and Rotational Kinetic Energy

A nuclear submarine propeller has a moment of inertia of $800.0 \text{kg} \cdot \text{m}^{2}$. If the submerged propeller has a rotation rate of 4.0 rev/s when the engine is cut, what is the rotation rate of the propeller after 5.0 s when water resistance has taken 50,000 J out of the system?

A solid sphere is rotating about an axis through its center at a constant rotation rate. Another hollow sphere of the same mass and radius is rotating about its axis through the center at the same rotation rate. Which sphere has a greater rotational kinetic energy?

(a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic energy of Earth in its orbit around the Sun?

A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 20.0 m/s at a distance of 0.480 m from the joint and the moment of inertia of the forearm is $0.500 \left( \text{kg}-\text{m}\right)^{2}$, what is the rotational kinetic energy of the forearm?

An aircraft is coming in for a landing at 300 meters height when the propeller falls off. The aircraft is flying at 40.0 m/s horizontally. The propeller has a rotation rate of 20 rev/s, a moment of inertia of $70.0 \left( \text{kg}-\text{m}\right)^{2}$, and a mass of 200 kg. Neglect air resistance so the rotation rate does not change as the propeller falls. (a) With what translational velocity does the propeller hit the ground? (b) What i…

A neutron star of mass $2 \times 10^{30} \text{kg}$ and radius 10 km rotates with a period of 0.02 seconds. What is its rotational kinetic energy?