Final answer:
Torque is calculated using the formula net T = Ia, where T is the torque, I is the moment of inertia, and a is the angular acceleration. For a force applied perpendicular to the radius with no friction, T = rF. Correct moment of inertia must be used for accurate calculations.
Step-by-step explanation:
To calculate the torque based off the moment of inertia, you can use the formula net T = Ia, where T represents the torque, I is the moment of inertia, and a is the angular acceleration. This is the rotational analog of Newton's second law. For a force applied perpendicular to the radius with negligible friction, torque can be calculated as T = rF, where r is the radius and F is the force applied.
The moment of inertia depends on the object's shape and mass distribution. For a hoop, it is calculated as I = MR2, where M is the mass and R is the radius. Care must be taken to use the correct moment of inertia for the object in question.
After calculating torque and ensuring you have the correct moment of inertia, apply the formula to find the angular acceleration. Always check to see if the calculated acceleration is reasonable based on your system of interest.