A flywheel is in the form of a solid disc of mass M= 6.0 kg and a radius of R= 0

Question

A flywheel is in the form of a solid disc of mass M= 6.0 kg and a radius of R= 0.16 m.  The flywheel is accelerated from rest to 60 RPM in 10 seconds with constant angular acceleration.  All frictional forces are negligible.  

a) Find the tangential speed of a point P on the rim of the flywheel at the end of 10 seconds after it started accelerating.

b) Find the tangential acceleration of the same point P on the rim of the flywheel at the end of 10 seconds after it started accelerating.

c)  Find the energy stored in the flywheel in the form of rotational kinetic energy at the end of 10 seconds after it started accelerating.

Please include all steps and formulas!!

Explanation / Answer

Angular velocity w = 2*pi*N/60 = 2*3.14*60/60 = 6.28 rad/s

Angular Acceleration = (w - w0)/t = (6.28 - 0)/10 = 0.628 rad/s^2

Moment of inertia I = 1/2*MR^2 = 1/2*6*0.16^2 = 0.0768 kg-m^2

a)

Tangential speed v = Rw

= 0.16*6.28

= 1.0048 m/s

b)

Tangential acceleration a = R*alpha

= 0.16*0.628

= 0.10048 m/s^2

c)

Rotational KE = 1/2*Iw^2

= 1/2*0.0768*6.28^2

= 1.514 J

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