A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s2. What is the kinetic energy of the shell after it has turned through 6.00 rev?

Solution 40E Step 1: Data given Mass of the spherical shell M = 8.20 kg Radius R = 0.220 m 2 Acceleration = 0.890 rad/s Revolution = 6.00 rev = 37.6 rad We shall find the inertia of the spherical shell It is given by I = (2/3) MR 2 Substituting values we get 2 I = (2/3) × 8.20 kg × (0.220 m) I = 0.26 kg m 2 Hence we have inertia as 0.26 kg m 2 Step 2 : We need to find the final velocity of the shell it is given by We know = 0i 2 2 f = +i2 f2 = 2 × 0.890 rad/s × 37.6 rad 2 = 66.92 rad /s 2 f f 8.18 rad /s Hence we have the final velocity of the spherical shell as 8.18 rad /s