Question

a solid disk of mass M and radius R is rotating on the vertical axle with angular speed. another disk of mass M/2 and radius R initially not rotating falls coaxially on the disk and sticks. the rotational velicity of this system after collision is

Answer 1

Solid disk of mass M

The radius of the disk R

Rotating with angular speed w1

Then the moment of inertia of the disk about an axis

I1=( MR^2)/2

Now the angular momentum of the system will be p1

P1 = I1* w1

P 1= (MR^2)w1/2 ..........(1)

Now another disk having mass M/2

Coaxially placed on previous disk having mass M

Now the total mass of the system will be M'

M' = M + M/2

M' = 3M/2

Then the moment of inertia of the system will be I2

Now the momentum will be

P2 = l2 w2

Now by the conservation of the momentum

P1 = P2

This is the rotational velocity after collision