Determine the change in rotational kinetic energy when the rotational velocity of the turntable of a stereo system increases from 0 to 33 rpm. Its rotational inertia is 6.8×10−3kg⋅m2 .

Answer 1

KE = 1/2*Iω^2

ω is the rotational velocity, but the unit is in rad/s. rpm means "revolutions per minute"
You need to convert 33 rpm to rad/s first:
33 rev/min = 33/60 rev/s = 0.55 rev/s
1 rev = 2π rad: => 0.55 rev/s*2π rad/rev = 0.55*2π rad/s = 1.1π rad/s ≈ 3.45575 rad/s

Now with the KE formula: KE = 1/2*Iω^2 = (1/2)*(6.0×10^-3)*(1.1π)^2 = 0.035827 J