Stepped Pulley: Angular and Linear Acceleration

[robert6774]

A stepped pulley is essentially a system of connected cocentric disks that have different radii. A stepped pulley (I= 2.0 kg*m^2) is placed on a frictionless axle and then strings are attached to two radii of 20 and 50 cm. The other ends of the strings are attached to a 2.0 and 1.0 kg mass respectively. Determine the angular acceleration of the pulley and the linear accelerations of the two masses.

I= 2.0 kg*m^2
r1= 50 cm
r2= 20 cm
m1= 1.0 kg
m2= 2.0 kg
w1= 0
w2= ?

I think I'm confusing the concept of the pulley starting at rest (so w1= 0) and the final angular speed (w2) of the rotating pulley with the fact that there are two different radii to be used in the same equation for the same pulley.

I'm pretty sure v= rw will come into play at some point but I need to find the angular speed in order to find the angular acceleration. And where the heck does time fit into all this?

I've also considered finding the linear accelerations and working the other way around but again I'm not sure how to look at this.

I've winged a couple ideas using the conservation of angular momentum and the conservation of angular kinetic energy but it doesn't make sense. Where do I start and how do look at/approach this problem?

 

[tiny-tim]

hi robert6774!

(have an omega: ω and an alpha: α and a tau: τ )

this is just forces, so use good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=26" …

F = ma for each mass, and τ = Iα for the pulley (with each v = rω, a = rα)

 

[robert6774]

Thank you tiny-tim for your help. I've just figured out how to use the Latex symbols, that should make my equations easier to read. The other Latex stuff is a bit more complicated, don't know if I'll need it.