# Does circular motion cause centripetal force OR does centripetal force cause circular motion?

1. Does circular motion cause centripetal force, or does centripetal force cause circular motion, or are they both occurring hand in hand together instantaneously?

2. One more question: If I project a body in such a way that an attractive force is being perpendicular to the velocity with which I projected the body, then would the body undergo circular motion?

• Note that in working exercises the phrase "[object] moves on a circular path" implies the existence of a centripetal force which may be of use in solving the problem. If your instructor has been talking about causation in that order if may be he was explaining the problem solving methodology. – dmckee --- ex-moderator kitten Mar 14 '15 at 17:11

If no force acts on a body it moves in a straight line. To make the body deviate from a straight line you have to apply a force to it. Therefore applying the centripetal force to the body is what makes it move in a circle.

If you apply a constant force at right angles to the direction of motion then your object will indeed move in a circle.

Physics does not have a proper, rigorous concept of causation. There are the terms locality and causality, but they are technical terms with precise meanings that do not occur in Newtonian physics.

Nevertheless, Newton's law, $\vec F = m \ddot{\vec x}$ is often seen to embody causation in a certain sense: You are given, as external circumstance, the total force $\vec F$, and you solve the equation for $\vec x$, so the force was there "before" the motion, or "causes" it.

All you need to know to describe the world is that whenever there is circular motion, there is a centripetal force, and that whenever there is a centripetal force, there is circular motion. But that is a tautology, because "centripetal force" is the force defined as the force acting such that the body it acts on follows a curved/circular path!

For the second question, not every attractive force will produce circular motion, but the usual forces with square laws like gravity or electromagnetism will produce circular/elliptical motion (unless you crash into the central body), as will forces that are constant and perpendicular to the velocity.

1. In a way centripetal force causes circular motion, centripetal force that accelerates a body to undergo circular motion. If you imagine a ball on a piece of string: when the ball is spun around the centripetal force will be tension, the tension of the string pulls the ball as it spins to cause it to move in a circle. Without the string, the ball will just go in a straight line; but without the motion of the ball, the tension of the string will still be there but the ball won't be moving in a circle which is why the statement that centripetal force causes circular motion is only partially true.

2. If you project a body in such a way it will only move in a circular motion if the force is of a certain magnitude and is coming from a stationary source. If your force is a rocket on the side of your ball, so the force moves with the ball, then you won't get circular motion. The magnitude of the force must be in accordance to this equation: $$F_c=mv^2/r$$ Where Fc is the force, m is the mass of your ball, v is the tangential velocity of your ball and r is the radius of your circle (from the source of the force to the ball). If these conditions are met, then you will get circular motion.

An example of this is an orbit, if you have your ball with mass and a planet of mass M then to get the ball into orbit using the force of gravity to act as the centripetal force you must find conditions in which the force of gravity is equal to the centripetal force. Gravitational force is given by: $$F_G=GMm/r^2$$ Where FG is the force of gravity, G is the gravitational constant, M is the larger mass (the mass of our planet), m is the smaller mass (the mass of our ball) and r is the distance from the planet to the ball. Using this equation and the centripetal force equation, we can work out under what conditions the force of gravity is equal to the centripetal force and therefore where we can get a circular orbit. $$mv^2/r=GMm/r^2$$ $$mv^2=GMm/r$$ $$v^2=GM/r$$ $$v=\sqrt(GM/r)$$

1. The force causes the change in velocity, not the other way round. It's how we define it. If you found in nature something that is under circular motion without any known forces being applied to it, we would have to examine the problem and define a new force.

What can cause confusion is that sometimes, it is easier to solve problems using a circular motion inertial frame. In such a system, no forces mean circular motion, and the centriFUGAL force is trying to get the object out of the motion.

2. Yes. The quintessential example is an moving electron in a magnetic field, as it is subject to a force perpendicular to both its velocity and the direction of the magnetic field: