Understanding Velocity and Acceleration of a Moving Particle

[WMDhamnekar]

A particle moves so that its position vector is given by $\vec{r}=\cos{(\omega t)}\hat{i} + \sin{(\omega t)}\hat{j}$. Show that the velocity $\vec{v}$ of the particle is perpendicular to $\vec{r}$ and $\vec{r} \times \vec{v}$ is a constant vector.

How to answer this question?

 

[topsquark]

First calculate \(\displaystyle \vec{v} = \dfrac{d \vec{r}}{dt}\). If \(\displaystyle \vec{r} \cdot \vec{v} = 0\) for all t then they are always perpendicular.

-Dan

 

[HOI]

Since the velocity function is the derivative of the position function and the acceleration function is the derivative of the velocity function, I would say, "start by taking a Calculus class!". Have you done that? Do you know what the derivatives of $cos(\omega t)$ and $sin(\omega t)$ are? Do you know how to show that one vector is perpendicular to another? (Dot product.)