Question

A 1000kg car has four 10kg wheels. When the cars moving what fraction of its total kinetic energy is due to rotation of the wheels about their axles? Assume that the wheels are uniform disks of the same mass and size. Why do you not need to know the radius of the wheels?

Answer 1

$$K=0.5Mv^2+0.5(4)I\omega^2$$

$$\omega=\frac{v}{r}$$

$$I=0.5mr^2$$

$$K=0.5Mv^2+0.5(0.5)(4)mv^2$$

The fraction of its total kinetic energy is due to rotation of the wheels about their axles is

$$\frac{0.5(0.5)(4)mv^2}{0.5Mv^2+0.5(0.5)(4)mv^2}=\frac{2m}{M+2m}=\frac{20}{1000+20}=0.0196$$

As it can be seen that the radius of the wheels cancel out it is not required.