Asphere of uniform density with mass 21 kg and radius 0.8 m is spinning, making one complete revolution every 0.8 s. the center of mass of the sphere has a speed of 8 m/s. (a) what is the rotational kinetic energy of the sphere?

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)