Question

A heavy flywheel rotating on its central axis is slowing down because of friction in its bearings. At the end of the first minute of slowing, its angular speed is 0.70 of its initial angular speed of 125 rev/min. Assuming constant frictional forces, find its angular speed at the end of the second minute.

Answer 1

Answer:

ωf' =5.16 rad/s

Explanation:

Given that

Initial angular speed ,ωi= 125 rev/min    ( 1 rev/min = 0.10472 rad/s)

ωi=13.08 rad/s

The angular speed after 1 min ,ωf= 0.7 x 125 = 87.5 rev/min

ωf=9.1 rad/s

Lets angular acceleration =α

We know that

ωf = ωi + α t

Now by putting the values in the above equation we get

9.1 = 13.08 + α x 60             ( after 1 min ,t= 60 s)

$\alpha =\dfrac{9.1-13.08}{60}$

α = -0.066 rad/s²

The angular speed after 2 min

ωf' = ωi + α t

ωf' =13.08 - 0.066 x 2 x 60 rad/s

ωf' =5.16 rad/s

Therefore the angular speed after 2 min will be 5.16 rad/s.