Force acting on the particle is always directed towards the center

AI Thread Summary
The discussion focuses on demonstrating that the force acting on a particle described by the elliptical equation r=acos(wt)i+bsin(wt)j is always directed towards the center. To prove this, it is suggested to differentiate the equation twice with respect to time to establish a relationship between the position vector and the acceleration vector. This approach will help in analyzing the direction of the force in relation to the center of the ellipse. Participants are seeking assistance in this mathematical proof. The goal is to confirm that the force consistently points inward towards the center of the ellipse.
Slayedr
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r=acos(wt)i+bsin(wt)j is the equation(it is an ellipse)

I need to somehow show that the force will always act towards the center.

Is there anyone who can possibly help?
 
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Slayedr said:
r=acos(wt)i+bsin(wt)j is the equation(it is an ellipse)

I need to somehow show that the force will always act towards the center.

Is there anyone who can possibly help?
Differentiate the equation twice with respect to t first of all, and see if you can relate the position vector to the acceleration vector.
 

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