In getting the moment of inertia, one has to know where the mass is located. Here you have two radii: how much mass is associated in each region of radaii?
So the net trorque= I w^2
and net torque= sum of both torques. Downward and to the right does not indicate direction ir relation to spin axis. You have to write in terms of clockwise, counterclockwise motion.
A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. (The moment of inertia of a uniform solid cylinder is I = ½ m r^2)
a) What is the angular acceleration of the cylinder?
b) How many revolutions does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?
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