Question

A flywheel has a mass of 5.0 kg, inner radius of 8.00 cm, and outer radius of 14.2 cm. Determine

a) angular frequency to store 400 kJ of rotational energy

b) the average power and torque delivered by the flywheel if 400kJ can be stored in 6.67 s

Answer 1

Moment of inetia of flywheel is given by

$I = \frac{1}{2}M(a^2 + b^2)$

$I = \frac{1}{2}*5*(0.08^2 + 0.142^2)$

a) Rotational KE is given by formula

$KE = \frac{1}{2}Iw^2$

$400*10^3 = \frac{1}{2}*0.06641*w^2$

b) Average power delivered is given by

$Power = \frac{Energy}{Time}$

$Power = \frac{400*10^3}{6.67}$

Now to find torque we can use equation below

$Power = \tau * \omega$

$5.99 * 10^4 = \tau * 3.47*10^3$

$\tau = 17.3 N.m$