Uniform circular motion (centripetal acceleration & force)

[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?

 

[jtbell]

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.

 

[V0ODO0CH1LD]

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.

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?

 

[Michael C]

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?

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.

 

[PJC01]

I would like to clarify that the scenario described does not involve uniform circular motion. In uniform circular motion, the velocity and acceleration vectors are always perpendicular to each other. In the scenario described, the acceleration vectors are not always perpendicular to the velocity vector, which means the motion is not uniform circular motion.

Furthermore, in uniform circular motion, the centripetal acceleration is the only force acting on the object, and it is always directed towards the center of the circle. In the scenario described, there are multiple forces acting on the object, and they are not all directed towards the center of the circle. Therefore, the acceleration experienced by the object is not a valid centripetal acceleration.

To achieve uniform circular motion, the object must experience a constant centripetal acceleration, which is equal to the square of the velocity divided by the radius of the circle. In the scenario described, the accelerations are constantly changing and are not equal to the required centripetal acceleration.

In conclusion, the object in this scenario is not experiencing uniform circular motion, and the accelerations applied are not valid centripetal accelerations. The object may appear to be in the same point in space, but its motion is not circular and therefore, cannot be considered uniform circular motion.