Physics

A cylinder having a mass of 3.5 kg can rotate about its central axis through point O. Forces are applied as shown: F1 = 9.0 N, F2 = 6.0 N, F3 = 3.0 N, and F4 = 4.0 N. Also, r = 5.0 cm and R = 12 cm.
Find the magnitude and direction of the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)

I'd need to know where the forces are applied and in what directions relative to the cylinder. You also have not defined r or R.

Add up the torques and use the equation

(Net torque) = (moment of inertia)x 9angular acceleration)

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