Question

Disk A, with a mass of 2.0 kg and a radius of 60 cm , rotates clockwise about a frictionless vertical axle at 40 rev/s . Disk B, also 2.0 kg but with a radius of 40 cm , rotates counterclockwise about that same axle, but at a greater height than disk A, at 40 rev/s . Disk B slides down the axle until it lands on top of disk A, after which they rotate together.

Answer 1

let
m1 = 2 kg
r1 = 60 cm = 0.6 m
w1 = -40 rev/s (clockwise)
I1 = 0.5*m1*r1^2

= 0.5*2*0.6^2

= 0.36 kg.m^2

m2 = 2 kg
r2 = 40 cm = 0.4 m
w2 = 40 rev/s (counter clockwise)
I2 = 0.5*m2*r2^2

= 0.5*2*0.4^2

= 0.16 kg.m^2

let wf is the final angular velocity of the two disks.

Apply conservation of angular momentum

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

wf = (I1*w1 + I2*w2)/(I1 + I2)

= (0.36*(-40) + 0.16*40 )/(0.36 + 0.16)

= -15.4 rev/s

|wf| = 15.4 rev/s <<<<<<<------Answer

negative sign indicates the disks rotate clockwise direction.