Question

Trucks can be run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 611 rad/s. One such flywheel is a solid, uniform cylinder with a mass of 551 kg and a radius of 1.1 m that rotates about its central axis. What is the kinetic energy of the flywheel after charging?

If the truck uses an average power of 6.5 kW, for how many minutes can it operate between chargings? (No units required.)

Answer 1

Angular kinetic energy E in Joules
E = ½Iω²
ω is angular velocity in radians/sec
I = moment of inertia in kg•m²

moment of inertia
I is moment of inertia in kg•m²
I = cMR²
M is mass (kg), R is radius (meters)
c = 1 for a ring or hollow cylinder
c = 2/5 solid sphere
c = ⅔ hollow sphere
c = ½ solid cylinder or disk around its center
c = 1/12 rod around its center, R = length
c = ⅓ for a rod around its end, R = length
c = 1 for a point mass M at a distance R from
the axis of rotation

I = ½550•1.1² = 332.7 kg•m²
E = ½Iω² = ½(332.7)(611)² = 6.21e7 J

6.5 kW = 6.5k J/s
6.21e7 J / 1e4 J/s = 5.37e3 sec = 62.10min