Using an analogy with the Newton's 2nd law for point masses, for rigid bodies, the external net torque on a rigid body, is equal to its rotational inertia (I), times the angular acceleration (α) of the body, as follows:
Since the magnitude of the torque is the product of the value of the force times the perpendicular distance between the line of action of the force and the axis of rotation, and the force is tangential to the rim of the disk, we can write the following expression:
For a solid disk, the rotational inertia regarding an axis through its center, and perpendicular to its face is as follows:
Replacing (3) in (1), and (2) in the left side of (1) also, we can solve for m, as follows:
The apple's acceleration is not influenced by the acceleration due to gravity for this question. In real life it most certainly is influenced by gravity.
