With axle and spokes of negligible mass and a thin rim a cer

With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel has a radius of 0.350 m and weighs 40.0 N; it can turn on its axle with negligible friction. A man holds the wheel above his head with the axle vertical while he stands on a turntable that is free to rotate without friction; the wheel rotates clockwise, as seen from above, with an angular speed of 55.0 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + man + turntable about the common axis of rotation is 1.50 kg·m^2. The man\'s free hand suddenly stops the rotation of the wheel (relative to the turntable). (a) Determine the resulting angular speed of the system. (b) Is the direction of the rotation clockwise or counterclockwise?

Solution

a)

Mass of wheel

M=F/g =40/9.8 =4.08 Kg

By Conservation of angular momentum

I₁W₁ = I₂W₂

Moment of inertia of bicycle is

I=MR²

=>W₂ =W₁*(I₁/I₂)

W₂ =55*(4.08*0.35²)/1.5

W₂ = 18.33 rad/sec

b)

The system rotates clockwise at the rate of 18.33 rad/s.