Heavy Pulley / Conservation of Mechanical Energy

[danrochester]

Homework Statement

A light inextensible string is wrapped around a cylindrical pulley of mass M that is free to rotate about its axis. The end of the string is attached to a block of mass m. Use conservation of mechanical energy to calculate the speed of the block after it has fallen a distance d starting from rest.

Homework Equations

Well this is the thing, I can easily write the equation for conservation of energy, but at some point I need to know omega, the angular velocity, which I don't think I have any way of knowing.

The Attempt at a Solution

I'm not looking for the answer here, just a hint. I can think of how to do this problem if I knew the radius of the pulley; then I could easily determine omega from v = omega*r. Is there a way to distribute the change in gravitational potential energy between the linear and rotational kinetic energies of the block and pulley that doesn't require any knowledge of the radius of the pulley?

 

[Doc Al]

Since v = ωr, you can express the angular velocity in terms of linear velocity. You don't need to know the actual radius.

 

[tiny-tim]

A light inextensible string is wrapped around a cylindrical pulley of mass M that is free to rotate about its axis.
…
I can think of how to do this problem if I knew the radius of the pulley; then I could easily determine omega from v = omega*r …

Hi danrochester!

(have an omega: ω )

You think you need the r to work out (1/2)Iω² …

but actually you can use v on its own, because the r² in the ω² cancels out with the r² in the I.

 

[danrochester]

no crap

haha thanks guys...Sometimes you keep digging until you're too deep to get out, and sometimes you just need to keep digging a liiiittle bit further...

 

[tiny-tim]

Homer Simpson's advice was …

No! Dig up! ​