Question

A particle moves in a circular path (radius=r) in the xy plane.
Suppose that at time t its positions are x(t) and y(t) respectively and $\theta$ is the angular position relative to the x axis measured in the counterclockwise sense, then x, y can be related to $\theta$ as

• A. $x=rsin\theta$ and $y=rcos\theta$
• B. $x=rcos\theta$ and $y=rsin\theta$
• C. $x=r^{2}cos\theta$ and $y=r^{2}sin\theta$
• D. $x=r^{2}sin\theta$ and $y=r^{2}cos\theta$

Answer 1

The correct option is B $x=rcos\theta$ and $y=rsin\theta$

Let the particle's instantaneous position be x(t) and y(t) and it makes an angle $\theta$ with the horizontal. As seen from the triangle, the $\frac{x}{r}=cos\theta ⟹x=rcos\theta$. Similarly, we can also write $\frac{y}{r}=sin\theta ⟹y=rsin\theta$
Thus the instantaneous position of the particle x and y are now expressed in terms of r and $\theta$. This is known as polar coordinates
Thus, option (b) is correct