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 ultra precise 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 (density 2.2 g/cm³), 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?