Here's the question:
A particle moves in a circle (center $0$ and radius $R$) with constant angular velocity $w$ counterclockwise. The circle lies in the $xy$ plane and the particle is on the $x$ axis at time $t = 0$. Show that the
particle's position is given by
$r(t) = \hat{x}R \cos(wt) + \hat{y}R \sin(wt)$.
Alright, so given anypoint $p$ on the circle, I can easily show that the the $x$ coordinate is given by $R\cos(wt)$ and the $y$ coordinate is given by $R\sin(wt)$.
I know that $\sin$ and $\cos$ functions get values between $-1$ and $1,$ so $p$ cannot be outside of the circle…but anyway I already assumed that $p$ was a point of the circle so I don't know why I bother with this.
I just can't convince myself that for all $t$ the point $p=(R\cos(wt),R\sin(wt))$ will be only on the circle.
Any minds? Thanks!
Best Answer
Isn’t it clear that the coordinates $(x,y)$ of $p(t)$ satisfy the equation $x^2+y^2=R^2$?