Why is the kinetic energy formula for this problem using the radius?

[pyroknife]

I attached the problem.

The solution is of the form:
.5*(5/32.2)v^2+.5(10/32.2)(12/18*v)^2 + 5*18/12*sin(60)-10*12/12*sin60=0

I don't understand why they put the radius in the kinetic energies like the 12/18 part. I know you have to do that, but I don't understand why.

 

[emailanmol]

Hey Pyroknife,

Please submit your approach to the solution first.