# Particle moving in a circle

haruspex
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Is this type of circular motion actually possible with the single force as shown in the picture ?
Yes. The necessary and sufficient condition that the motion is controlled by such a force is one of the equations needed to arrive at the desired equation.
Is this some sort of planetary motion around the sun with perigee coinciding the focus
No. The trajectory would need to be an ellipse with the source of the force at one focus. Yes, a circle is a special case of an ellipse but its focus would be at the centre, not on the circumference.

Do you think If I write the two eq of motions then I should end up with a circular path ?

But since type of force is unknown how to do that ?

I am curious as to how this force makes the particle move in a circle .

haruspex
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Gold Member
Do you think If I write the two eq of motions then I should end up with a circular path ?

But since type of force is unknown how to do that ?

I am curious as to how this force makes the particle move in a circle .
You do not know the magnitude of the force towards the origin, but you do know the magnitude in another direction.

but you do know the magnitude in another direction.
Which direction ?

haruspex
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Gold Member
Which direction ?
I'd like you to think that through for yourself. It's not hard.

In a direction perpendicular to the line joining C and the particle P at any instant ?

How does that help ?

haruspex
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In a direction perpendicular to the line joining C and the particle P at any instant ?
Yes. So what equation can you write?

ehild
Homework Helper
Please explain how do we infer this from the question .
It was a guess, you do not know the magnitude of the force. But you can see that the radial component is zero, and the tangential part changes sign at C.
You can imagine a force, proportional to the distance between points C and P.

Yes. So what equation can you write?
Sorry . I don't know . Can you tell what needs to be done .

haruspex