A ring (4 kg, r = 1 m) rotates in a CW direction with initial angular velocity 2

Question

A ring (4 kg, r = 1 m) rotates in a CW direction with initial angular velocity 20 s-1. A disk (4 kg, r = 1 m) rotates in a CCW direction with initial angular velocity 40 s-1. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.

What is the initial angular momentum Li of the ring+disk system?
kg m2 s-1

What is the final angular velocity ?f of the ring+disk system?
s-1

Explanation / Answer

Angular momentum is given by

L = I*w

I(ring) = m*r^2

I(disk) = m*r^2/2

Li(system) = Li(ring) + Li(disk)

Li = m*r^2*wi(ring) + (m*r^2/2)*wi(disk)

wi(disk) = 40 rad/sec

wi(ring) = -20 rad/sec

Li = 4*1^2*(-20) + (4*1^2/2)*40

Li = 0 kg-m^2/sec

Part B

using angular momentum conservation

Li = Lf (since Li = 0)

Lf = If*wf = 0

wf = 0 rad/sec

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