Question

Disk A, with mass of 2.0 kg and a radius of 40 cm, rotates clockwise about a frictionless vertical axle at 30 rev/s. Disk B, aslo 2.0 kg but with a radius of 20 cm, rotates counterclockwise about the same axle, but a greater height than disk A, at 30 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 their common angular speed (in rev/s) and in which direction do they rotate?

Answer 1

Clockwise rotation induces a negative angular momentum at right angles to the spinning disk, while anti-clockwise rotation induces a positive angular mementum. Angular momentum L=I⍵ where I=moment of inertia=mr²/2 for a solid disk, and m is its mass and r its radius.

⍵=30revs/sec=60π radians / sec.

For disk A, L=-9.6π and disk B, L=2.4π mks.

Combined ang momentum initially=-7.2π.

Combined moments of inertia=0.16+0.04=0.20.

If ⍵ is the final angular velocity: final AM=initial AM, 0.20⍵=-7.2π, ⍵=-36π=18 revs/s clockwise.