Flywheels are discs rotating on nearly frictionless (sometimes magnetic) bearing

Question

Flywheels are discs rotating on nearly frictionless (sometimes magnetic) bearings, used for storing energy.
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?

PLEASE EXPLAIN/JUSTIFY METHOD OF SOLVING

Explanation / Answer

v^2 - u^2 =2*a*s
v = *r

given final  = 4*10^3 rpm = 4*10^3/(2*pi)*60 rad/s

s = no.of revolutions * 2 *pi *r = 2000 * pi * r

a = v^2 /2*s

a = (4*10^3/(2*pi) *60)^2*r^2/(2000*pi*r)

a = 232 211.048* r m/s^2

when  1 = 2*10^3 rpm

distance reavelled = v1^2/2*a =  (2*10^3/(2*pi) *60)^2*r^2/( 23211 .048*r) = 500*pi*r

No. of revolutions = s/2*pi*r = 250

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