This is actually from my physics class, but it's the algebra that's the problem. It's been driving me insane. So we're doing torque problems.
$\Sigma\tau = I \alpha $
We're routinely replacing the angular acceleration (alpha) with its equivalency, $a/R$ so that $ \alpha = a/R$, where $a$ is the tangential acceleration and $R$ is the radius.
The moment of inertia, $I$, includes an $R^2$ term: some fraction times mass times radius squared.
My professor always cancels out all the R terms here, leaving just a fractional $ma$, mass times acceleration. This is the part I don't understand. Why isn't there an R left over in the numerator?