How Is the Total Kinetic Energy of a Car Calculated?

[fishingspree2]

Homework Statement

The 4 wheels of a car each weigh 25kg and have a radius of 0,3m. Without its wheels, the car weighs 10^3 kg. The wheels are homogenous cylinders. What is the total kinetic energy of the car and the wheels if the car is moving at a speed of 30 m/s?

Homework Equations

$$K_{tot}=4(0.5I_{CM}\omega^{2}+0.5MV_{CM}^{2})+K_{car}$$
the first to terms of the last question concern the wheels
$$I_{cylinder}=\frac{MR^{2}}{2}$$
$$\omega=\frac{V_{CM}}{R}$$

The Attempt at a Solution

replacing omega by V/R, I by MR^2/2 and distributing the 4:
$$K_{tot}=MV^{2}+2MV^{2}+\frac{10^{3}\times30}{2}$$
$$K_{tot}=25\times30^{2}+50\times30^{2}+\frac{10^{3}\times30}{2}=82,2 \mathrm{kJ}$$
The right answer is 518 kJ

where is the mistake? :(
thank you, sorry for my english

 

[Doc Al]

The Attempt at a Solution

replacing omega by V/R, I by MR^2/2 and distributing the 4:
$$K_{tot}=MV^{2}+2MV^{2}+\frac{10^{3}\times30}{2}$$

You forgot to square the speed in that last term.

 

[fishingspree2]

Thank you very much
sorry for the waste