Question

A hoop, a solid cylinder, a solid sphere, and a thin, spherical shell each have the same mass of 4.01 kg and the same radius of 0.260 m. (a) What is the moment of inertia (in kg · m2) for each object as it rotates about its axis

Answer 1

Given that

Radius ,r= 0.26 m

Mass ,m= 4.01 kg

Moment of inertia of hoop

I= m r²

`I=4.01* 0.26^2\ kg.m^2`

`I=0.271\ kg.m^2`

Moment of inertia of solid cylinder

`I=(1)/(2)mr^2`

`I=(1)/(2)* 4.01* 0.26^2\ kg.m^2`

`I=0.135\ kg.m^2`

Moment of inertia of solid sphere

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

`I=(2)/(5)* 4.01* 0.26^2\ kg.m^2`

`I=0.108\ kg.m^2`

Moment of inertia of thin spherical

`I=(2)/(3)mr^2`

`I=(2)/(3)* 4.01* 0.26^2\ kg.m^2`

`I=0.18\ kg.m^2`