Full Solution 8: Rotation Flywheels are discs rotating on nearly frictionless (s

Question

Full Solution 8: Rotation
Flywheels are discs rotating on nearly frictionless (sometimes magnetic) bearings, used for storing
energy (we'll see rotational kinetic energy in Chapter 9).
Suppose a certain flywheel makes 1000 (= 1.0×103) complete revolutions while accelerating from rest
to 4.0×103 rpm. Did the wheel make more than, less than, or exactly 500 revolutions in accelerating
from rest to 2.0×103 rpm, which is half the final velocity? If not 500 revolutions, then what fraction of
the final 1000 rev did it make during this interval?

Explanation / Answer

Angular displacement made in 1000 complete revolutions = 1000*2* radians

Now, we're given the angular velocity = 4.0*103*2 radians

So if we consider uniformly accelerated angular motion, the equations of motion that apply to motion of a particle in a st. line still apply.

So we have

v2 - u2 = 2 a s

we know that u=0

So substituting v=4.0*103*2 s=1000*2

We get a = 16*103 radian/min

Now again we are asked to find the number of rotation when the wheel hits 2.0*103 rotations/min or 2.0*103*2 radian/min

again apply the same equation

now we get s=500 radian

Which is equal to 500/2 rotations = 250 rotations are completed when the wheel reaches the speed of 2.0*103 rpm

this is 1/4 of the final no.of rotations.

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