Find Mass of Pulley: Solve with Torque & Impulse Calculations

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To find the mass of the pulley in this problem, one must analyze both the pulley and the falling stone using Newton's second law. The stone's acceleration can be determined from its final speed and distance fallen, which is essential for relating the pulley’s mass to the system's dynamics. The net torque on the pulley is calculated using the formula net torque = I * alpha, where I is the moment of inertia and alpha is the angular acceleration. The moment of inertia for a solid cylinder is given by I = m * r^2 / 2. By combining these equations, the mass of the cylinder can be derived from the acceleration of the stone.
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Homework Statement


A light string is wrapped around the outer rim of a solid uniform cylinder of diameter 75.0cm that can rotate without friction about an axle through its center. A 3.00kg stone is tied to the free end of the string. When the system is released from rest, you determine that the stone reaches a speed of 3.50m/s after having fallen 2.50m.

What is the mass of the cylinder?

Homework Equations


net torque = I * alpha
I = m * r^2 / 2


The Attempt at a Solution


For this problem I have no idea where to start. I am completely lost...I know there should be some Omega calculations a theta calculations and I need to find impulse along with torque...any help is appreciated!
 
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You need to analyze both the pulley and the falling stone. Write Newton's 2nd law for each, then combine the equations to relate pulley mass to the acceleration of the stone.

Use the given data to determine the acceleration of the stone.
 

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