3. Th e \"governor\" of many mot ay cording to the rotating speed of the motor S

Question

3. Th e "governor" of many mot ay cording to the rotating speed of the motor Suppose we have a flywheel in the shape of a solid cylinder (1- 5MR') its mass is 20 kg, and while rotating at a speed of 5 rev/sec its radius is measured to be 08 meters. The engine is then revved and the flywbeel's mass spreads out so that the new radius of the cylinder is 16 meters a. Find the new angular speed of the spinning flywheel AND STATE THE PRINCIPLE OF PHYSICS you use to obtain your answer. during this process? Explain your answie b. Does the rotational kinetic energy of the fly wheel increase, decrease, or remain the same

Explanation / Answer

Ii = 0.5 M (0.08^2)

wi = 5 rev/s

If = 0.5 M (0.16^2)

Applying angular momentum conservation,

Ii wi = If wf

0.08^2 x 5 = 0.16^2 wf

wf = 1.25 rev/s .....Ans

(b) kinetic energy decreases.

(c) Applying energy conservation,

PEi + KEi = PEf + KEf

m g h + 0 = 0 + m v^2 /2 + I w^2 /2

m g h = m v^2 /2 + (m r^2)(v/r)^2 /2 = m v^2

v = sqrt( g h)

v = 9 m/s

(d) if it does not roll, then all potential will go into translationl kE.

mv ^2 /2 = m g h

v = sqrt(2 g h)

but when rolls, some energy goes into rotational Ke also.

hence Speed will be more.

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