Disk conservation of momentum problem

[BrainMan]

Homework Statement

A disk with momentum of inertia I1 rotates with angular velocity Wi about a vertical friction less axle. A second disk, with moment of inertia I2 and initially not rotating , drops onto the first. Because the surfaces are rough, the two eventually reach the same angular velocity, w. (a) calculate w.(b) show that mechanical energy is lost in this situation and calculate the ration of the final to the initial kinetic energy.

Homework Equations

The Attempt at a Solution

I successfully calculated the angular velocity as wi(I1/I1 +I2) = w but am having trouble on the second part which is to find the ratio of final to kinetic energy. I not really sure how to approach that part.

 

[Orodruin]

What is the final kinetic energy and what is the initial one? Take the ratio.

 

[BrainMan]

What is the final kinetic energy and what is the initial one? Take the ratio.

The final kinetic energy should just be Ke = 1/2(I1+I2)w^2. The initial should be 1/2IW_i^2. How do I take the ratio?

 

[haruspex]

The final kinetic energy should just be Ke = 1/2(I1+I2)w^2. The initial should be 1/2IW_i^2. How do I take the ratio?

You write a ratio as two expressions separated by a colon. As with division, you can cancel any common factors. Substitute for w using the result of the first part of the question.

 

[BrainMan]

You write a ratio as two expressions separated by a colon. As with division, you can cancel any common factors. Substitute for w using the result of the first part of the question.

OK thanks! I got it right!