Question

A baseball bat is 32 inches (81.3 cm) long and has a mass of 0.96 kg. Its center of mass is 22 inches (55.9 cm) from the handle end. You hold the bat at the very tip of the handle end (the knob) and let it swing in simple harmonic motion. What is the bat’s moment of inertia if its period of oscillation is 1.35 seconds?

Answer 1

Answer:

0.24 kgm²

Explanation:

$L$ = length of the bat = 81.3 cm = 0.813 m

$m$  = mass of the bat = 0.96 kg

$d$  = distance of the center of mass of bat from the axis of rotation = 55.9 cm = 0.559 m

$T$  = Period of oscillation = 1.35 sec

$I$ = moment of inertia of the bat

Period of oscillation is given as

$T = 2\pi \sqrt{\frac{I}{mgd}}$

$1.35 = 2(3.14) \sqrt{\frac{I}{(0.96)(9.8)(0.559)}}$

$I$ = 0.24 kgm²