Suppose you exert a force of 150 N tangential to the outer edge of a 1.31-m radi

Question

Suppose you exert a force of 150 N tangential to the outer edge of a 1.31-m radius 73.5-kg grindstone (which is a solid disk). Part (a) What is the torque tau, in newton meters, you are exerting on the grindstone, relative to the center of mass of the grindstone? tau = Part (b) What is the angular acceleration of the grindstone alpha_0, in radians per square second, assuming negligible friction? Part (c) What is the angular acceleration of the grindstone alpha_f, in radians per square second, if there is an opposing factional force of 21 N exerted 0.35 m from the axis?

Explanation / Answer

a)
T = F*r
    = 150*1.31
    = 196.5 Nm

b)
Moment of inertia, I = 0.5*m*r^2
                                            = 0.5*73.5*(1.31)^2
                                            = 63.1 Kgm^2
use:
T = I*ao
196.5 = 63.1*ao
ao =3.12 rad/s^2

c)
Net F = 150 - 21 = 129 N
T = F*r = I*af
129*1.31 = 63.1 * af
af = 2.68 rad/s^2

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