I have two equations. The first is for all of the forces on a hanging mass from a pulley. The second is for the sum of the torques about the pulley from which the mass hangs. I simply have to combine the equations to find the acceleration of the object. I have attempted every algebraic manipulation I can think of and keep coming out with the wrong answer. Please help.
T-mg=ma (for the sum of forces on the hanging mass)
Tr=I(-a/r) (for the torques about the pulley)
Here, T is tension, m is the mass of the hanging object, a is the acceleration, r is the radius of the pulley, I is the moment of inertia of the pulley.
I'm supposed to combine the two equations to eliminate T and solve for a.
The Attempt at a Solution
OK, solve equation 1 for T.
T = ma + mg
Cool, now plug into equation 2.
a = -(gmr^2)/(I)-g
I keep coming out with the same exact solution every time, but it is apparently wrong. Can someone tell me where I went wrong?