Question

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 kg core, 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.

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?

Find the moment of inertia of a uniform 3.2 kg ball with diameter 0.216 m.

Part C

Complete previous part(s)

Answer 1

a)

the total moment of inertia is given by

I_Total =(2/5)MR²+(2/3)mr²

I_Total =(2/5)(1.6)(0.196/2)² + (2/3)(1.6)(0.206/2)²

I_Total =0.01746 Kg-m²

b)

I=(2/5)MR² =(2/5)(3.2)(0.216/2)²

I=0.01493 Kg-m²