Need help with physics homework?

Question

A wheel of radius R = 29.9 cm, mass M = 2.86 kg, and moment of inertia I is mounted on a frictionless, horizontal axle as in the figure. A light cord wrapped around the wheel supports an object of mass m = 0.518 kg.

The wheel was being winded up initially, and the mass is measured to have an upward speed of 3.62 m/s. At that moment, the wheel is let go on its own, starts slowing down and eventually reverses its direction when the mass pulls it down. What is the maximum height, h, the mass will rise above the point at which it is released?

http://www.webassign.net/serpop/10-20.gif

I think that this is a conservation of energy problem, but all of the types of energy seem to be hard for me to keep track of. There's linear kinetic energy and then rotational kinetic energy UGH! Please help!!!

Answer 1

when the mass is released, it has its linear kinetic energy mv^2/2.  The disk has its rotational kinetic energy (i don't know the equation, you should have it).  It is something like m*k*w^2 where k is a constant for a disk w is the rotational speed in radians/second (i think), and m is mass.  You can calculate the rotation from the speed of the mass (it is going at the same speed as the outside of the disk).  

Add those up, and the sum will be equal to the amount of potential energy transfered to the mass.  you should be able to calculate the distance from that.  

Since it is YOUR homework, I'll leave the calculation to you.  They key is both the rotational energy and the linear kinetic energy are transformed into work on the mass.