Question

A 1090 kg car has four 12.7 kg wheels. When the car is moving, what fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles? Assume that the wheels have the same rotational inertia as uniform disks of the same mass and size.

Answer 1

`(KE_(Rotational))/(KE_(Total)) = 0.018`

Step-by-step explanation:

To develop this exercise we proceed to use the kinetic energy equations,

In the end we replace

`KE_(Total)=KE_(Translational)+KE_(Rotational)`

`KE_(Total)=(1)/(2)m_(car)+4*(1)/(2)*I*((v)/(r))^2`

Here

`I=(1)/(2)m_(wheels)*r^2` meaning the 4 wheels,

So replacing

`KE_(Rotational)=4(1)/(2)*((1)/(2)m_(wheels)*r^2)*((v)/(r))^2=m*v^2`

So,

`(KE_(Rotational))/(KE_(Total)) = (m_(wheels)*v^2)/((1)/(2)m_(car)*v^2+m_(wheels)*v^2)`

`(KE_(Rotational))/(KE_(Total)) = (m_(wheels))/((1)/(2)m_(car)+m_(wheels))`

`(KE_(Rotational))/(KE_(Total)) =  (10)/(545+10)`

`(KE_(Rotational))/(KE_(Total)) = 0.018`