A bowling ball is far from uniform. Lightweight bowling balls are made of a relatively low-density core surrounded by a thin shell with much higher density. A 7. 0 lb (3. 2 kg) bowling ball has a diameter of 0. 216 m; 0. 196 m of this is a 1. 6 kgcore, surrounded by a 1. 6 kg shell. This composition gives the ball a higher moment of inertia than it would have if it were made of a uniform material. Given the importance of the angular motion of the ball as it moves down the alley, this has real consequences for the game
. (a)Model a real bowling ball as a 0. 196-m-diameter core with mass 1. 6 kg plus a thin 1. 6 kg shell with diameter 0. 206 m (the average of the inner and outer diameters) What is the total moment of inertia?Express your answer with the appropriate units.
(b)Find the moment of inertia of a uniform 3. 2 kg ball with diameter 0. 216 m. Express your answer with the appropriate units.