A uniform solid disk with a mass of 21.4 kg and a radius of 0.167 m is free to r

Question

A uniform solid disk with a mass of 21.4 kg and a radius of 0.167 m is free to rotate about a frictionless axle. Forces of 90.0 and 125 N are applied to the disk, as the figure illustrates. Taking the clockwise direction to be the negative direction, what is (a) the net torque produced by the two forces and (b) the angular acceleration of the disk?

The 125 N Force is acting in the clockwise direction to the center of mass at a 90 degree angle, while the 90 N Force is acting in a counterclockwise direction to the center of mass, also at a 90 degree angle.

Explanation / Answer

Let ' r' be radius, ' M' be mass of solid disk.
Net Torque is T=[125*r] - [90*r]
=35*r = 5.845 N*m ( since r = 0.167 m)
We have T= I *a where I=M(r^2)/2 is the moment of Inertia of the disk and 'a' is the angular acceleration. I = (21.4)*([0.167]^2)/2 = 0.298kg*m^2
So, a=5.845/0.298= 19.614 rad/s^2.

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