Torque and Angular Acceleration for a Rigid Body Problem

Yosty22

1. 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.

2. Homework Equations

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

3. 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

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tiny-tim

Homework Helper
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

Homework Helper
Gold Member
2018 Award
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.

"Torque and Angular Acceleration for a Rigid Body Problem"

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