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

Answer:

The moment of inertial of the wheel,  $I = 8(\frac{1}{3}M_sL^2 ) + M_rL^2$

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 $=\frac{1}{3}M_sL^2$

Moment of inertial of the wheel

$I = 8(\frac{1}{3}M_sL^2 ) + M_rL^2$