Question

A steel disc ( S) spins on about a frictionless spindle on a frictionless air table.

The steel disc has a radius of R=0.24m and a mass ms=6.15kg, and may be modelled as solid with a uniform mass distribution.

The steel plate has an initial angular velocity of ω0=4.4rad/s.

A stationary aluminium disc of identical size and shape, and a mass of ma=2.11kg is dropped onto the steel disc from a small height.

After a brief duration the two discs rotate together.
a) Determine the final angular velocity of both disks.
b) Determine the final total kinetic energy of the two discs.

Answer 1

This is the diagram:

Answer 2

I was able to calculate the initial kinetic energy of the rotating steel disc to be equal to 1.715J, but don't know how to move forward. Tried many methods but all turn out wrong.

Answer 3

you are looking to get the initial angular momentum of the steel disc

then that should be the same as the final angular momentum of both discs.

you cannot assume that energy is conserved. eg it is friction that causes them to end up travelling at the same rate and friction si energy loss....

angular momentum is \(L = I \omega\)

Answer 4

Thank you very much, hadn't read the question properly (that they ended up rotating at the same speed).