Physics help????

Question

Your friend is enjoying riding around on their novelty unicycle. Its wheel has an inner radius 2.8 m and an outer radius of 2 m and a mass of 11.5 kg (model it as a thick hoop rotating about its center). They try to move the fastest they can. They accelerate from rest over a distance of 38 m. If you clock their final linear speed at 13 m/s, how much rotational work did they do on the wheel?

Answer 1

Moment of inertia of annular disc = 1/2 M ( R ₂ ² - R₁ ² ) = 1/2 * 11.5 ( 2.8 * 2.8 - 2 * 2 ) = 8.96 kg m²

Work done = Change in Rotational Kinetic energy = 1/2 I ( wf ² - wi ²) , I Moment of Inertia

wf = Final angular velocity and wi = Initial angular velocity = 0

Angular Velocity ( final + = Linear velocity / Outer radius of disc

Plug in values

Rotational KE = 1/2 ( 11.2/2 )(2.8 * 2.8 - 2*2 ) ( 13*13/(2.8*2.8) J

= Work done = 2.8 *1.6 *( 169/7.84) = 96.6 J