A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a uniform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr².

a) If such a flywheel of radius r₁ = 0.75 m and mass m₁ = 24 kg can spin at a maximum speed of v = 35 m/s at its rim, calculate the maximum amount of energy, in joules, that this flywheel can store.

b) Consider a scenario in which the flywheel described in part (a) (r₁ = 0.75 m, mass m₁ = 24 kg, v = 35 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r₂ = 1.1 m and mass m₂ = 11 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel.

c) Return now to the flywheel of part (a), with mass m₁, radius r₁, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed v_car. Enter an expression for the mass of the car, in terms of the quantities defined here.