Question

In: Physics

A solid disk of mass M and radius R is rotating on the vertical axle with...

A solid disk of mass M and radius R is rotating on the vertical axle with angular speed w. Another disk of mass M/2 and radius R, initally not rotating, falls coaxially on the disk and sticks. The rotational velocity of this system after collision is:

w

w/2

2w/3

3w/2

2w

Expert Solution

Mass of the first disk = M

Radius of the first disk = R

Moment of inertia of the first disk = I₁

I₁ = MR²/2

Initial angular velocity of the first disk = ₁ =

Mass of the second disk = M/2

Radius of the second disk = R

Moment of inertia of the second disk = I₂

I₂ = (M/2)R²/2

I₂ = MR²/4

Initial angular velocity of the second disk = ₂ = 0 rad/s

Final angular velocity of both the disk = ₃

By conservation of angular momentum,

I₁₁ + I₂₂ = (I₁ + I₂)₃

(MR²/2)() + (MR²/4)(0) = (MR²/2 + MR²/4)₃

₃ = 2/3

Rotational velocity of the system after the collision = 2/3

genius_generous answered 1 year ago

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