# Math20512

## Individual questions

#### For the period of motion I still get a little confused. Is it always $$P=2\pi\omega$$ with $$\omega=v/r$$ or does it depend on the system ?

Answer in two parts:
(a) for circular motion, the angular speed $$\omega$$ measures the number of radians per second. So how long does it take to do a full revolution ((2\pi\) radians)? Answer: $$2\pi/\omega$$. Right?
(b) For simple harmonic motion, the general solution is something like $$u(t) = A\cos(\omega t)+B\sin(\omega t)$$ - this usually has nothing to do with circular motion, so $$\omega$$ is not $$v/r$$. But the period of $$u(t)$$ is what? Again, it is $$2\pi/\omega$$. Because $$u(t+2\pi/\omega)=u(t),$$ right?
The similarity is why the same letter is traditionally used for angular speed and (angular) frequency.

Page last modified on Sun, 22 April 2012, at 22:39 (BST)
Search jam - wiki