Atwood Machine :

eqs={
m1 g - t1 == m1 a1,
m2 g - t2  == m2 a2,
t1 r - t2 r == i3 α,
a1==-a2,
a1==r α}

Solve[eqs,{a1,a2,α,t1,t2}] /.{i3 ->(1/2)m3 (r^2)} //Simplify