An experimental flywheel, used to store energy and replace an automobile engine,

Question

An experimental flywheel, used to store energy and replace an automobile engine, is a solid disk of mass 185 kg and radius 0.400 m. What is its rotational inertia?

When driving at 23.1 m/s (51.7 mph), the fully energized flywheel is rotating at an angular speed of 3176 rad/s. What is the initial rotational kinetic energy of the flywheel?

If the total mass of the car is 1026 kg, find the ratio of the initial rotational kinetic energy of the flywheel to the translational kinetic energy of the car.

If the force of air resistance on the car is 680 N, how far can the car travel at a speed of 23.1 m/s (51.7 mph) with the initial stored energy? Ignore losses of mechanical energy due to means other than air resistance.

Explanation / Answer

rotational inertia = 0.5 * mass * radius^2

rotational inertia = 0.5 * 185 * 0.4^2

rotational inertia = 14.8 kg.m^2

rotational kinetic energy = 0.5 * moment of inertia * angular speed^2

rotational kinetic energy = 0.5 * 14.8 * 3176^2

rotational kinetic energy = 74643622.4 J

rotational kinetic energy / translational kinetic enegy = 74643622.4 / (0.5 * 1026 * 23.1^2)

rotational kinetic energy / translational kinetic enegy = 272.678

by conservation of energy

initial energy = final energy

74643622.4 + (0.5 * 1026 * 23.1^2) = 680 * distance

car can travel 110172.594 m

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