Question

how do I convert rotational acceleration to linear acceleration in a conveyer belt system?

Answer 1

Remember that we can derive this relationship using the equation for arc length:\[\large \text{Zeroth Derivative:}~~~\huge s=r\theta\]\[\large \text{First Derivative:}~~~\huge v=r\omega\]\[\large \text{Second Derivative:}~~~\huge a=r\alpha\]

Answer 2

\(a\) is the linear acceleration
\(\alpha\) is the radial acceleration

So therefore, the linear acceleration of the disc/washer (also will be the acceleration of the belt) is directly proportional to the radial acceleration.