So basically there is a wheel with a radius of 0.3 m. A light cord wrapped around the wheel supports a 0.75-kg object that accelerates at 3 m/s^-2 downwards. What is the moment of inertia of the wheel? (no friction)
The Attempt at a Solution
Seems like it should be an easy question, but the inclusion of the acceleration threw me off. The two approaches I have thought about are:
I=mr^2, I=(0.3*0.75^2) which gives an option in the answers (0.15), but that seems too easy and I did not use the acceleration.
The other approach is using Torque=I (angular acceleration), using the above value for inertia (0.15), and then calculating angular acceleration by r * linear acceleration (0.3*3), but this produced a number not in the solution list (0.135).
Are there other approaches I have missed? Involving forces or the like?