Centripetal Force - How to describe it?

[superdave]

So I had a thought today, and I wanted to figure out if it's correct or not about centripetal force.

I've always heard it described as the inward force something experiences as it goes around a curve. But could it better be described as the force necessary for an object to maintain circular motion at a given radius and velocity? Because F_c always has to be accounted for with other forces (tension, gravity, friction).

So F_c is not a force itself like friction or gravity is. It's just what we call whatever real force/forces is/are causing the inward acceleration that causes circular motion.

This came about because someone was asking if centripetal force is inward, Newton's Third Law should have an outward force as well. I expained that the outward force is on whatever is causing the inward force (on the other end of the string, the object being orbitted, the other frictious surface, etc...). This led to the fact that F_c is always caused by something else, which led to the fact that F_c = mv^2/r is just a way for us to know what force is necessary to maintain the circular motion for a given r and v, but it doesn't actually account for the force.

 

[jtbell]

So F_c is not a force itself like friction or gravity is. It's just what we call whatever real force/forces is/are causing the inward acceleration that causes circular motion.

Correct, "centripetal" doesn't indicate a new type of force like friction, tension, etc. It's simply an adjective that indicates the direction of the force. In general, it's not even a single force that's involved here, but rather the net force on an object that is moving in a circular path. It's easy to construct situations where no single force points towards the center of the circle, but the net force does.

 

[mikeph]

could it better be described as the force necessary for an object to maintain circular motion at a given radius and velocity?

precisely

 

[superdave]

Alright, thanks. I'm student teaching now in a HS Physics class. I wanted to make sure my thinking was correct before I passed it on to the students.

 

[rcgldr]

Note the path of the object doesn't have to be circular. The centripetal force is the component of force perpendicular to the path (velocity) of an object at an instant in time. If the non-centripetal component of force is zero at all times, then the object moves at constant speed, but it's path could be almost any shape: circle, ellipse, spiral, parabola, hyperbola, sin wave, ... . As an example, imagine the possible paths a car could take while moving at constant speed with just steering inputs.

 

[superdave]

Note the path of the object doesn't have to be circular. The centripetal force is the component of force perpendicular to the path (velocity) of an object at an instant in time. If the non-centripetal component of force is zero at all times, then the object moves at constant speed, but it's path could be almost any shape: circle, ellipse, spiral, parabola, hyperbola, sin wave, ... . As an example, imagine the possible paths a car could take while moving at constant speed with just steering inputs.

Yes, I can see how that's true. Though at the high school level, we generally only deal with uniform circular motion (constant centripetal force).

 

[rcgldr]

This came about because someone was asking if centripetal force is inward, Newton's third law should have an outward force as well.

One exception to this is a two body system where two objects orbit circularly about a common center of mass. In this case, the Newton third law pair of forces is the gravitational force that accelerates the first object towards the second object, and the gravitational force that accelerates the second object towards the first object, and both forces are "inwards".

Though at the high school level, we generally only deal with uniform circular motion (constant centripetal force).

I wasn't sure if you also considered elliptical orbits, where gravitational force includes a non centripetal component, except at the ends points of the major axis.

 

[harrylin]

[..] the outward force is on whatever is causing the inward force (on the other end of the string, the object being orbitted, the other frictious surface, etc...). This led to the fact that F_c is always caused by something else [..]

Newton called that, I think, the force of inertia which acts in reaction to acceleration, and it is centrifugal (the term "centrifugal force" is often used with a completely different meaning, causing much confusion).

One exception to this is a two body system where two objects orbit circularly about a common center of mass. In this case, the Newton third law pair of forces is the gravitational force that accelerates the first object towards the second object, and the gravitational force that accelerates the second object towards the first object, and both forces are "inwards". [..]

Yes indeed; the objects can similarly orbit circularly attached to each other by a rope or spring. For each object there is a 3d law force pair but the details such as the points where the forces act depend on the situation.