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

`I=4.13* 10^(-3)\ kgm^2`

Step-by-step 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=(C)/(2\pi)`

`r=(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=(2)/(5)mr^2`

`I=(2)/(5)* 0.1417* (0.27)^2`

`I=0.00413\ kgm^2`

`I=4.13* 10^(-3)\ kgm^2`

So, the moment of inertia of a baseball is
`4.13* 10^(-3)\ kgm^2`. Hence, this is the required solution.