A flywheel is being used to start a piece of large machinery. The way it works i

Question

A flywheel is being used to start a piece of large machinery. The way it works is that the flywheel is brought up to speed (1500 rpm) and then smoothly coupled with the drive axis of the machine, after which the flywheel and drive axis rotate as one. The flywheel is a solid disk with a mass of 2 kg and a radius of 1 meter, and the drive axis has a moment of inertia of 9 kg middot m^2. If angular momentum is conserved, what is the angular velocity of the combined system after the coupling procedure?

Explanation / Answer

w1 = 1500 rpm

moment of inertia of solid disk I = 0.5 mr^2

m = 2 kg, r = 1m

from conservation of angular momentum

I1w1 = I2w2

(0.5mr^2)w1 = (0.5mr^2 +Id)w2

(0.5*2*1^2)*1500 = (0.5*2*1^2 +9)*w2

w2 = 150 rpm

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