With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel

Question

With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel has a radius of 0.380 m and weighs 42.0 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 63.0 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + man + turntable about the common axis of rotation is 2.50 kg·m2. 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?

dont round any numbers

Explanation / Answer

radius r = 0.38 m
wight W = 42 N
rotatinoal inertia of the system I = 2.5 kg m^2

intiial angular speed of the wheel, wo = 63 rad / sec

rotatinoal moment of inertia of the wheel = mr^2 = Wr^2/g = 42*0.38^2/9.81 = 0.6182262 kg m^2
hence
from conservation of angular momentum
let the final angular spped of the system be w
then
Iw = Wr^2*wo/g
2.5*w = 0.618*63
w = 15.5736 rad/s

this angular speed is clockwise just like the previous angular speed for the conservstion of angular momentum

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