In Fig. 10-65, a cylinder having a mass of 3.0 kg can rotate about its central axis through point O. Forces are applied as shown: `F_(1)=6.0N,F_(2)=4.0N,F_(3)=2.0NandF_(4)=5.0N`. Also, r = 5.0 cm and R = 12 cm. Find the (a) magnitude and (b) direction of the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)

Explanation

(a) `6.5rad//s^(2)`, (b) The direction is counterclockwise (which is the positive sense of rotation).