A gymnast does cartwheels along the floor and then launches herself into the air, executing several flips in a tuck while she is airborne. Her moment of inertia when executing the cartwheels is 13.5 kg⋅m2 and her spin rate is 0.50 rev/s. If her moment of inertia in the airborne tuck is 3.4 kg⋅m2 and she completes the flips in 2.0 s, how many revolutions does she undergo in the air?
A cylinder with rotational inertia kg⋅m2 rotates clockwise about a vertical axis through its center with angular speed rad/s. A second cylinder with rotational inertia kg⋅m2 rotates counterclockwise about the same axis with angular speed rad/s. The cylinders are coupled, after which they have the same rotational axis.
What is the angular speed of the coupled cylinders?
What percentage of the cylinders’ original kinetic energy is lost to friction during coupling?
A ride at a carnival has four 15-m-long, 200-kg-mass spokes attached to a central axis of rotation. At the end of each spoke is a pod of mass 100 kg that can hold two people. If the ride spins at 0.2 rev/s with each pod holding two 50-kg-mass children, what is the ride’s spin rate with empty pods?