Torque and Angular Acceleration for a Rigid Body Problem

[Yosty22]

Homework Statement

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 2.00kg and diameter 0.500m. After the system is released, find (a) The tension in the wire on both sides of the pulley, (b)the acceleartion of the box, and (c)the horizontal and vertical components of the force that the axle exerts on the pulley.

Homework Equations

Torque=R (cross) F = I \alpha
Newton's Laws

The Attempt at a Solution

I started with free body diagrams and writing out equations. For mass 1, the 12 kg box on the table, the only forces acting in the x direction are T₁. On the hanging mass, m₂, the only forces are the weight of the hanging mass and T₂. I tried to figure out the torque about the pulley, using τ=I \alpha. I=.5mr² and \alpha = a/r, so Torque = .5mr²*(a/r). However, I don't really know what to do from there. I figure both of the tensions create a torque, but I'm not sure what I need to do from here.

Any help would be greatly appreciated

 

[tiny-tim]

Hi Yosty22!

I figure both of the tensions create a torque …

That's correct.

Find the torque from each tension …

their difference is the total torque that you've just found.

 

[Yosty22]

Oh, duh. Thanks a lot, tiny-tim. Much appreciated. :)

 

[haruspex]

Fwiw, there are a couple of important details missing from the problem statement:
- That the wire is horizontal from the 12kg block to the pulley.
- That the pulley is only frictionless in relation to its axle; in relation to the wire it has unlimited(?) friction.