Question

A baseball has a weight of five ounces and a circumference of 9 inches. Assuming it has a uniform density, what is the moment of inertia of a baseball? Give your answer in LaTeX: kg\cdot m^2k g ⋅ m 2.

Answer 1

Answer:

$I=4.13\times 10^{-3}\ kgm^2$

Explanation:

It is given that,

Weight of baseball, W = 5 ounces

Since, 1 ounce = 0.0283 kg

W = 0.1417 kg        

Circumference of the baseball, C = 69 inches = 1.7526 meters

$C=2\pi r$

$r=\dfrac{C}{2\pi}$

$r=\dfrac{1.7526}{2\pi}$

r = 0.27 meters

Assuming it has a uniform density, we know that the moment of inertia of the object in its entire volume is given by :

$I=\dfrac{2}{5}mr^2$

$I=\dfrac{2}{5}\times 0.1417\times (0.27)^2$

$I=0.00413\ kgm^2$

$I=4.13\times 10^{-3}\ kgm^2$

So, the moment of inertia of a baseball is $4.13\times 10^{-3}\ kgm^2$. Hence, this is the required solution.