Question

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t=0t=0, the wheel turns through 8.75 revolutions in t=t= 13.0 ss . At 13.0 ss the kinetic energy of the wheel is 36.0 J Part A For an axis through its center, what is the moment of inertia of the wheel? Express your answer with the appropriate units.

Answer 1

Answer:

The moment of inertia is 1.01 kg m²

Explanation:

Given:

θ = 8.75 revolutions = 2π * 8.75 = 54.98 rad

t = time = 13 s

Ek = kinetic energy = 36 J

The angular acceleration is equal to:

$\alpha =\frac{\theta }{0.5t^{2} } =\frac{54.98}{0.5*13^{2} } =0.65rad/s^{2}$

The angular velocity is:

w = αt = 0.65 * 13 = 8.45 rad/s

The moment of inertia is:

$I=\frac{2E_{k} }{w^{2} } =\frac{2*36}{8.45^{2} } =1.01kgm^{2}$