Good approximation! Often when we apply equations to calculate moment of inertia, we are...

Good approximation! Often when we apply equations to calculate moment of inertia, we are making a useful approximation, such as when we approximate a wagon wheel as a disk without a hole in the center. A manufactured item exists that is extraordinarily spherical, where the approximation of a uniform sphere is astonishingly close. Gravity Probe B is a satellite-borne experiment that uses ultraprecise gyroscopes to detect the warping of space–time due to the rotation of the Earth’s gravitational field as predicted by Einstein. Each gyroscope uses a sphere made of fused quartz 38 mm in diameter, which is so spherical that were it scaled to the size of the Earth, the difference between hills and valleys would be less than 4 m! The sphere of a gyroscope spins at 10,000 rpm about an axis through its center. (a) What is the kinetic energy of the sphere? (b) What is the angular momentum of the sphere?