Question

A 8 kg disk with a radius of 1 meters has several forces applied to it as shown in the sketch. F1 is 41 N and is applied at the edge of the disk, F2 is 7 N is applied at 1/4 the radius from the center of the disk, F3 is 5 N is applied at 3/4 the radius from the center, F4is 29 N is applied at the edge of the disk, and, lastly, F5 is 16 N and is applied at the edge of the disk at an angle of 23 degrees. If the moment of inertia about the center for the disk is I = 1/2 M R2, and the disk is initially spinning at 36 rad/s counter-clockwise its center,  how long, in seconds, does it take the disk to be spinning at 10 rad/s counter-clockwise about its center?

F3 F 2 F4 F1

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