# Thread: Particle travelling in a circle.

1. ## Particle travelling in a circle.

Hello,
I've been doing problems based on a particle traveling around in the unit circle. Say we have a particle traveling in the unit circle, starting at (1,0) at time t = 0 and with a speed of t and time t. The particle is traveling in the direction of increasing $\displaystyle \theta$. The question asks to find the velocity and acceleration vector at the point (0,1). I can do this.

I was wondering, what would happen if we had all of the same information as above, except that the particle was traveling on an ellipse given by, say, $\displaystyle x^2 + 2y^2 = 1$. How would you find the velocity or acceleration vectors? Is it the same method as finding those vectors in the unit circle?

2. Originally Posted by Silverflow
Hello,
I've been doing problems based on a particle traveling around in the unit circle. Say we have a particle traveling in the unit circle, starting at (1,0) at time t = 0 and with a speed of t and time t. The particle is traveling in the direction of increasing $\displaystyle \theta$. The question asks to find the velocity and acceleration vector at the point (0,1). I can do this.

I was wondering, what would happen if we had all of the same information as above, except that the particle was traveling on an ellipse given by, say, $\displaystyle x^2 + 2y^2 = 1$. How would you find the velocity or acceleration vectors? Is it the same method as finding those vectors in the unit circle?

See this Wiki snippet for info on parametric equations of an ellipse.

Ellipse - Wikipedia, the free encyclopedia

To go from r(t) to v(t) and a(t), it's the same method as for a circle. Take the derivative of each component. This won't show what dy/dx is though immediately, you will have dx/dt and dy/dt.

3. Thanks for that. It makes sense.