Distance covered by a wheel in time t rotating at a certain angular frequency - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-09-20T08:21:45Z https://physics.stackexchange.com/feeds/question/270520 https://creativecommons.org/licenses/by-sa/4.0/rdf https://physics.stackexchange.com/q/270520 -1 Distance covered by a wheel in time t rotating at a certain angular frequency Siddharth Thevaril https://physics.stackexchange.com/users/70235 2016-07-29T08:34:46Z 2016-07-30T17:42:14Z <p>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</p> <blockquote> <p>Given a wheel of radius $r$, rotating at $n$ times per second, how much distance will it cover in $T$ seconds?</p> </blockquote> <p>The way I solved it -</p> <p>rotations per second = $n/sec$</p> <p>$\therefore$ distance covered in 1 sec = $2\pi rn$</p> <p>$\therefore$ distance covered in $T$ sec = $2\pi rnT$</p> <p>Did I do this correctly?</p> https://physics.stackexchange.com/questions/270520/-/270529#270529 1 Answer by varivirva for Distance covered by a wheel in time t rotating at a certain angular frequency varivirva https://physics.stackexchange.com/users/120558 2016-07-29T09:23:19Z 2016-07-29T09:29:07Z <p>Let us assume that the wheel does not slip. If this assumption holds true then the following holds:</p> <p>$\omega$rt=x .</p> <p>Now let us find $\omega$ </p> <p>given that the wheel turns n times in one second, this would mean the wheel turns 2$\pi$n rad every second thus </p> <p>$\omega=2\pi$n rad/sec</p> <p>So the answer you seek is </p> <p>x=2$\pi$nrt, where </p> <p>x is the distance travelled [m]</p> <p>n is the rotation frequency [1/s]</p> <p>r is the radius of the wheel [m]</p> <p>t is time [s]</p> <p>Yes your initial answer is correct.</p>