Mass Pulley System, Acceleration

[ryankunzzz]

Homework Statement

A block of 1kg is resting on an incline of 20° that has a coefficient of friction μk=0.45 with the surface. It is connected with a mass less string to a friction-less pulley of mass 0.10 kg to a hanging block of 2 kg. What is the acceleration of the system without ignoring rotational inertia. Model the pulley as a disk.

Homework Equations

First we need Newtons 2nd law, ΣF=ma
Also for rotational motion ΣF=Iα
and friction is ƒk=μN where N is the normal force.

The Attempt at a Solution

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After drawing my free body diagrams, I was left with this :

But I'm stumped there, I feel like I'm missing something obvious.

I want to plug the two equations for the tensions into the pulley equation, but then I'm still missing the radius of the pulley.

EDIT: The -m2g in the last equation on the right should be m2a

EDIT #2: I forgot the R on the (T2-T1)=IAlpha, I solved it. Thanks.

 

[Simon Bridge]

Well done ... and good work doing all the algebra before subbing in the values.