# Calculating omega as a function of time for a flywheel

1. Dec 4, 2011

### dannyR

hiya all, I've done a experiment which was hanging a mass from a light string wrapped around the axis of a flywheel. The mass was released and the flywheel began to rotate.

during calculations ive found out it would be great to have ω as a function of time and ive been stuck about how to get this.

could I do a force diagram using F=ma?, but then im unsure of the mass "m".
would I use the mass which is falling and add the moment of inertia of the flywheel or is this very wrong? :(.

or could I use energy stored such as

mgh=1/2Iω2+1/2mr2ω2+K

mgh, loss in potential energy of the falling mass

kinetic energy in the flywheel

kinetic energy in the falling mass

where K would be the frictional force i think it would be proportional to ωr

could i replace h the height the mass has fallen by using the F=ma bit i talked about above then replace h=1/2at2 then solve for t or ω??

ive thought about this alot and always been stopped by not knowing how to calculate something or use F=ma with moment of inertia stuff could someone please point me in the right direction?

Thanks alot Danny