# Uniform circular motion (centripetal acceleration & force)

1. May 24, 2012

### V0ODO0CH1LD

Imagine a body moving to the right with velocity v, I then apply a force that accelerates the body leftwards by v and downwards by v.
After one second, the body has stopped moving to the right and is only moving downwards with velocity v.
Then, while I keep accelerating the body to the left until it reaches a velocity v leftwards, I also accelerate the body upwards until it has stopped moving downwards.
By that point, I accelerate the body to the right by v and up by v, after one second it has stopped its movement to the left and is now only moving up.
Finally, I apply a acceleration of v downwards until it stops moving up and rightwards until it reaches a velocity of v to the right.
The object is now exactly in the same point in space it started. And I repeat the same process again and again.

My question is: providing I start the next step at the exact moment I finish the previous one, will the object experience uniform circular motion?
And in that case, clearly those accelerations are less then the centripetal acceleration the body would experience going in the exact same circular fashion. So why is that not a valid centripetal acceleration?

2. May 24, 2012

### Staff: Mentor

What you've described is not uniform circular motion. The magnitude of the force and acceleration are constant as in uniform circular motion, but their direction changes discontinuously, unlike uniform circular motion.

I haven't worked out the path in detail, but I think it would consist of four parabolic segments, one for each stage of constant force direction; not a circle.

3. May 24, 2012

### V0ODO0CH1LD

So even if it did go around in the same circular path it wouldn't be considered uniform circular motion because the direction of the force and acceleration doesn't cycle neatly?

4. May 24, 2012

### Michael C

Your example does not go in a circular path. As jtbell says, the path will consist of four parabolic segments.

If an object does go in a circular path at a constant speed, then it is by definition in uniform circular motion. In this case, the acceleration of the object will always be towards the centre of the circle, unlike in your example.

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