A flywheel designed to power a vehicle has mass 200 kg and i

A flywheel designed to power a vehicle has mass 200 kg and is in the shape of a hoop with radius 1 m. A) If it is rotating at a rate of 60, 000 RPM, how much rotational kinetic energy does it have? B) If energy was taken away at the rate of 10 horsepower, how long would the energy last?

Solution

moment of inertia

I = m * r^2

I = 200 * 1^2 = 200 kg-m^2

omega 1 = 60000 rpm = 6280 rad/s

A)

Rotational kinetic energy K = 1/2 * I * omega^2

K = 0.5 * 200 * 6280^2

k = 3.94 * 10^9 J

B)10 horsepower = 7460 J/s

dk/dt = I * omega * d(omega)/dt

7460 = 200 * 6280 * d(omega)/dt

d(omega)/dt = alpha = 0.006 rad/s^2

time t= omega 1 / alpha

t = 6280/0.006

t = 1046666.66 s

t = 290.74 hrs