Question

A 2.0 kg bicycle wheel with a radius of 0.40 m turns at a constant angular speed of 28 rad/s when a 0.35 kg reflector is at a distance of 0.2 m from the axle. What is the angular speed of the wheel when the reflector slides to a distance of 0.3 m from the axle?

Answer in 3 decimal places, and include full equation please.

Answer 1

Using Angular momentum conservation:

Li = Lf

Ii*wi = If*wf

Ii = Initial moment of inertia = M*r^2 + m*r1^2

M = mass of wheel = 2.0 kg

r = radius of wheel = 0.40 m

m = mass of reflector = 0.35 kg

ri = intial distance of reflector from axis = 0.2 m

wi = initial angular velocity = 28 rad/sec.

If = final moment of inertia = M*r^2 + m*rf^2

rf = final distance of reflector from axis of rotation = 0.3 m

So,

(M*r^2 + m*ri^2)*wi = (M*r^2 + m*rf^2)*wf

wf =wi*(M*r^2 + m*ri^2)/(M*r^2 + m*rf^2)

wf = 28*(2*0.4^2 + 0.35*0.2^2)/(2*0.4^2 + 0.35*0.3^2)

wf = 26.606 rad/sec.

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