A flywheel is a solid, rotating disk that is sometimes used to store energy. The

Question

A flywheel is a solid, rotating disk that is sometimes used to store energy. The moment of inertia for a solid disk is 1/2MR^2 where M is the mass and R is the radius. If a flywheel weighs 15kg and has a radius of 0.8m, determine the following.
  
A) If a point on the outside of the disk is moving at 6 m/s, what is the angular velocity of the flywheel?
  
B) If the flywheel starts from rest and accelerates at a constant rate for 60 s to bring it up to the angular velocity found in Part A, what is the angular acceleration?
  
C) If the angular acceleration in Part B is generated by a constant force applied tangentially to the outside edge of the disk (as shown below), what is the magnitude of the force?
  

Explanation / Answer

Part A)

w = v/r

w = (6)/(.8)

w = 7.5 rad/s

Part B)
Apply wf = wo + (alpha)t

7.5 = 0 + alpha(60)

alpha = .125 rad/s^2

Part C)
Apply Torque = I(alpha) and FL, Thus

(.5mr^2)(.125) = F(r)

.5(15)(.8)(.125) = F

F = .75 N

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