Acceleration of a pulley. Torque, and moment of inertia.

[EV33]

Homework Statement

There are two blocks, one of mass m1 and the other of m2. They are connected by a rope that runs over a pully of radius R and interia I. m2 slides down a frictionless incline at an angle theta, and m1 hangs virtically while being pulled up by the tension in the rope. Find the expression for acceleration.

Homework Equations

Fnet=m2gsin(theta)-m1g
F/M=a

The Attempt at a Solution

With the previous two equations I came to this conclusion...

(m2gsin(theta)-m1g)/(m1+m2+I)

The right answer has I/R^2 instead of just I.

I figured it would be just I because the mass of an object is its inertia.

Howwoud I derive the I/R^2?

 

[ideasrule]

How did you get an equation with an "I" when your initial equations:

Fnet=m2gsin(theta)-m1g
F/M=a

didn't have an "I" anywhere? Anyhow, for mechanics problems, you should always draw free-body diagrams for every object (including the pulley!), write down Newton's second law for each object, and then solve the resulting equations. That way, you'll see very clearly where the I/R^2 came from.

 

[EV33]

I got the I from thinking that I of the pulley would be the same thing as mass for the blocks because isn't mass just the inertia of an object? and I put my net force over the total mass.

I think I may have figured it out but I also may be making a mistake here...

T1 and T2 are equal to the tensions on each side, and alpha=a/R

T2R-T1R=Ialpha

R(T2-T1)=Ialpha

Tnet=I(a/R)/R

ma=Ia/(R^2)

m=I/R^2