Trucks can be run on energy stored in a rotating flywheel, with an electric moto

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 683 rad/s. One such flywheel is a solid, uniform cylinder with a mass of 465 kg and a radius of 1.5 m that rotates about its central axis. What is the kinetic energy of the flywheel after charging? What is the formula for the moment of inertia of a solid cylinder rotating about its central axis? If the truck uses an average power of 6.7 kW, for how many minutes can it operate between chargings? (No units required.)

Explanation / Answer

here m = 465Kg R = 1.5 m W = 683 rad / s

1. Angular kinetic energy E in Joules
E = ½I²
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 / 2 for solid cylinder

so I = 1 / 2 x 465 x 1.52

= 523.125 Kg x m2   Ans

so the energy

E = 1 /2 x 523.125 x 683

= 178647.1875 j Ans

2. the average power P = 6.7 Kw

as we know that

P = W / t

t = 178647.1875 / 6.7 x 1000

t=26.6637 sec=0.44439 min

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