Does changing the diameter of the rear wheels impact both the speed and acceleration of a mouse trap car on the race track?

Question

anonymous · Answer

Jaja, do you mean something like the image below? (It's cool)

By definition, velocity written in term of radius is:

$\large{v = r\omega}$

Where $\omega$ is the change in angular velocity (the change in angle in a given time). As you can see, if the angular velocity is fixed, you can increase the velocity just by increasing the radius of the wheels.

And sice $\large{a = \frac{v}{t}}$, by pluging the above equation here we have $\large{a = \frac{r\omega}{t}}$. $\large{\frac{\omega}{t}}$ is the angular acceleration: $\alpha$. And so for a given $\alpha$, you can increase the tangential acceleration $a$ just by increasing the radius too.

Since you are increasing the radius of just the rear wheels and the others are still small, these are going to spin faster than larger ones because of this: $\large{\frac{v}{r}= \omega}$ (the velocity is the same but the radius is small, and hence $\omega$ is greater for those wheels.