Rational dynamics (physics)?

Question

Suppose you exert a force of 217 N tangential to a 0.315 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.)
(a)
What torque (in N · m) is exerted? (Enter the magnitude.)
  N · m
(b)
What is the angular acceleration (in rad/s2) assuming negligible opposing friction? (Enter the magnitude.)
  rad/s2
(c)
What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 21.6 N exerted 2.00 cm from the axis? (Enter the magnitude.)
rad/s2

oldschool · Accepted Answer

(a) 
What torque (in N · m) is exerted? (Enter the magnitude.)
Torque = Force at 90° to radius * radius
Torque = F*r = 217*0.318 = 69.0 N ∙ m <<<<<< (a)
(b) 
What is the angular acceleration (in rad/s2) assuming negligible opposing friction? 
Moment of Inertia I = ½mr² = ½*75*0.315² = 3.72kg∙m²
Torque = I*α --> α = Torque/I = 69/3.72 = 18.5rad/s² <<<<< (b) 
(c) 
What is the angular acceleration (in rad/s2) if there is an opposing frictional force of 21.6 N exerted 2.00 cm from the axis?
Net Torque = 69 - 21.6*0.02 = 69 - 0.432 = 68.574
α = Net Torque/I = 68.574/3.72 = 18.4rad/s² <<<<< (c)

Rational dynamics (physics)?

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