# Distance covered by a wheel in time t rotating at a certain angular frequency

I'm a web developer who has lost his touch with Physics 6 years ago and now I'm implementing a certain animation, I just want to know whether I'm calculating it correctly

Given a wheel of radius $r$, rotating at $n$ times per second, how much distance will it cover in $T$ seconds?

The way I solved it -

rotations per second = $n/sec$

$\therefore$ distance covered in 1 sec = $2\pi rn$

$\therefore$ distance covered in $T$ sec = $2\pi rnT$

Did I do this correctly?

• Hello Siddharth : Please note this is not a "homework" site. We do not solve homework, and we do not check your answers. You can find our policy on this here. – sammy gerbil Jul 30 '16 at 17:44

## 1 Answer

Let us assume that the wheel does not slip. If this assumption holds true then the following holds:

$\omega$rt=x .

Now let us find $\omega$

given that the wheel turns n times in one second, this would mean the wheel turns 2$\pi$n rad every second thus

$\omega=2\pi$n rad/sec

So the answer you seek is

x=2$\pi$nrt, where

x is the distance travelled [m]

n is the rotation frequency [1/s]

r is the radius of the wheel [m]

t is time [s]

Yes your initial answer is correct.