Question

A wagon wheel consists of 8 spokes of uniform diameter, each of mass ms and length L cm. The outer ring has a mass mring. What is the moment of inertia of the wheel

Answer 1

The moment of inertial of the wheel,
`I = 8((1)/(3)M_sL^2 ) + M_rL^2`

Step-by-step explanation:

Given;

8 spokes of uniform diameter

mass of each spoke, =
`M_s`

length of each spoke, = L

mass of outer ring, =
`M_r`

The moment of inertial of the wheel will be calculated as;

`I = 8I_(spoke) + I_(ring)`

where;

`I_{spoke` is the moment of inertia of each spoke

`I_{ring` is the moment of inertia of the rim

Moment of inertia of each spoke
`=(1)/(3)M_sL^2`

Moment of inertial of the wheel

`I = 8((1)/(3)M_sL^2 ) + M_rL^2`