A futuristic design for a car is to have a large disklike flywheel within the car storing kinetic energy. The flywheel has mass 370 kg with a radius of 0.50 m and can rotate up to 540 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1600 kg car, find the maximum attainable speed of the car.

Explanation:

Rotational kinetic energy of flywheel

= 1/2 Iω² where I is moment of inertia , ω is angular velocity

for wheel I = 1/2 m R² where m is mass and R is radius of flywheel

Putting the values

I = 1/2 x 370 x .5²

= 46.25 kg m²

ω = 2πn where n is frequency of revolution per second

ω = 2 x 3.14 x 540 = 3391.2

Rotational kinetic energy = .5 x 46.25 x 3391.2²

= 265.94 x 10⁶ J

If this energy is transferred to a car of mass 1600kg , velocity acquired by it be v , then

kinetic energy of car = rotational kinetic energy of flywheel

= 1/2 m v ² =  265.94 x 10⁶

.5 x 1600 v² = 265.94 x 10⁶

v² = 33.24 x 10⁴

v = 5.76 x 10²

= 576 m /s

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