Question

You set out to design a car that uses the energy stored in a flywheel consisting of a uniform 80-kg cylinder of radius r that has a maximum angular speed of 430 rev/s. the flywheel must deliver an average of 2.00 kj of energy for each kilometer of distance. find the smallest value of r for which the car can travel 300 km without the flywheel needing to be recharged.

Answer 1

E = 300km * 2000J/km = 600000J

The rotational energy is given by:
E = 0.5 * I * ω² 

I for a uniform cylinder is given by:
I  = 0.5 * m * r²

Resulting equation:
E = 0.25 * m * r² * ω²

Given values:
ω = 430 rev/s = 430 * 2π / s
E = 600000

Solve for r.