Question

A wheel has a horizontal axis and a moment of inertia I = 220.0 kg۰m². A rope is wrapped around the rim of the wheel, R = 0.230 m, and the free end of the rope has a 4.00 kg mass attached to it. The system is released from rest. Draw free-body diagrams for both the wheel and the 4.00 kg mass. Determine the angular acceleration α of the wheel.

Answer 1

steps:
is done, the free-body diagram for 1 and 2
For 1.
concepts apply torque.
1. The concept touch equals

the force of the torque on the wheel is the tension of the string T
2. concept torque equals
equations are combined.

acceleration experienced by the mass equals the tangential acceleration of the wheel.

2.

Newton's second law applies.

the net force is also equal to the sum of all forces. Tencion weight down and up.
the expression of tension is obtained
combined with the equation obtained for one.
finally evaluated numerically

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free body diagram

For the wheel acts an  support force up and the weight of the wheel down, in addition to the tension of the string.

For the mass of 4 kg. acting weight and tension.