Question

A bus contains a 1440 kg flywheel (a disk that has a 0.63 m radius) and has a total mass of 10200 kg. Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 21 m/s in rad/s, assuming 90.0% of the rotational kinetic energy can be transformed into translational energy.

Answer 1

Answer:
`\omega =93.51 rad/s`

Step-by-step explanation:

Given

mass of Flywheel
`m_1=1440 kg`

mass of bus
`m_b=10200 kg`

radius of Flywheel
`r=0.63 m`

final speed of bus
`v=21 m/s`

Conserving Energy i.e.

0.9(Rotational Energy of Flywheel)= change in Kinetic Energy of bus

Let
`\omega`be the angular velocity of Flywheel

`0.9\cdot (I\omega ^2)/(2)=(m_bv^2)/(2)`

`I=moment\ of\ Inertia =mr^2=1440\cdot 0.63^2=571.536 kg-m^2`

`0.9\cdot (571.536\cdot \omega ^2)/(2)=(10200\cdot 21^2)/(2)`

`\omega ^2=21^2* (10200)/(0.9* 571.536)`

`\omega =21* 4.45=93.51 rad/s`