Question

A bus contains a 1,509 kg flywheel (a disk that has a 1.8 m radius) and has a total mass of 18,563 kg. Assume 90.0% of the rotational kinetic energy of the flywheel can be transformed into translational energy of the bus. what is the angular velocity in unit of round per minute the flywheel must have to contain enough energy to take the bus from rest to climb a hill of height 24.0 meters and still have a speed of 7.7 m/s at the top of the hill? Use g = 10 m/s2.

Answer 1

here,

the mass of flywheel , m1 = 1509 kg

the mass of Bus , m2 = 18563 kg

for height h = 24 and final velocity , v = 7.7 m/s

let the iniital speed of Bus be u

using conservation of momentum

0.5 * m * u^2 = 0.5 * m * v^2 + m * g * h

0.5 * u^2 = 0.5 * 7.7^2 + 9.81 * 24

u = 23.03 m/s

let the angular velocity of flywheel be w

as per given information

0.9 * ( rotational kinetic energy of flywheel) = kinetic energy of bus

0.9 * ( 0.5 * I * w^2) = 0.5 * m2 * u^2

0.9 * ( 0.5 * (0.5 * m * r^2) * w^2) = 0.5 * m2 * u^2

0.9* (0.5 * 1509 * 1.8^2 * w^2) = 18563 * 23.03^2

solving for w

w= 4.5 rad/s

the angular speed is 4.5 rad/s