Constants Disk A, with a mass of 2.0 kg and a radius of 90 cm , rotates clockwis

Question

Constants Disk A, with a mass of 2.0 kg and a radius of 90 cm , rotates clockwise about a frictionless vertical axle at 20 rev/s . Disk B, also 2.0 kg but with a radius of 60 cm , rotates counterclockwise about that same axle, but at a greater height than disk A, at 20 rev/s . Disk B slides down the axle until it lands on top of disk A, after which they rotate together.

After the collision, what is magnitude of their common angular velocity (in rev/s)?

In which direction do disks rotate after the collision?

Explanation / Answer

Using law of conservation of angular momentum

initial angular momentum = Final angular momentum

I1*w1 + I2*w2 = (I1+I2)*w

I1 = 0.5*M1*R1^2 = 0.5*2*0.9^2 = 0.81 kg-m^2

I2 = 0.5*M2*R2^2 = 0.5*2*0.6^2 = 0.36 kg-m^2

then

(-0.81*20)+(0.36*20) = (0.81+0.36)*w

w = -7.69 rev/s

so answer is 7.69 rev/s clockwise

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