Rotational kinetic energy of a disk

[physgirl]

ok, so a thread with hanging mass at the end is wrapped around a disk. the disk is dropped and mass is released. how do you find the kinetic energy of the weight at a given time/distance fallen from the disk? I'm not sure to whether use rotational kinetic energy or linear kinetic energy... all the basic values are given, except for the moment of inertia of the disk... so how would I find the kinetic energy of the mass at a given time after its release?

 

[Astronuc]

It depends on the what happens when "the disk is dropped and mass is released."

If the disk and mass are dropped together, they are both subject to the same acceleration, g, unless there is more air resistance (force) on the disc.

Obviously, the kinetic energy of the mass if given by 1/2mv², so one must determine the velocity of the mass as a function of time or distance traveled.

If the mass is moving relative to the disk, then one would need to determine the difference in velocity (speed) of the mass with respect to the rotational axis of the disk, and this speed difference would be manifest in the rotation of the disk, and the differential speed would be related to the angular velocity of the disk.

Note - the acceleration of any mass in 'freefall' is limited by the local acceleration due to gravity.