How do you determine which force is the centripetal force in a problem?

Answer 1

Centripetal force is a resultant force. Never draw centripetal force on a free-body diagram. For example, if you attached a string to a ball and rotate it, the tension is the string provides centripetal force. If you ride a gravitron, the normal force from the wall provides the centripetal force.

Answer 2

Centripetal force P is, by definition, the force that points inward towards the center of rotation. But having said that, keep in mind that centrifugal force F, which is a faux force, is equal in magnitude but opposite in direction to centripetal force whenever there is no acceleration of the rotating mass m along the radius of turn R.

Thus, for example, when swinging a toy top of mass m around your head at tangential velocity v from a string R long, you have P = C = mv^2/R. P, the centripetal force, pulls the mass towards the center of the rotation; and the string in fact is doing that pulling on the top. That's a real string doing a real pull...centripetal force is real.

But if there were only P, the top would accelerate into the center of rotation. Why? Because f = P = ma; and a > P/m and the mass would accelerate a along the tug of the string.

But for every force there is an equal but opposite force. For P there is an F...but only when the mass is fixed at R while rotating. Thus, f = P - F = 0 = ma because F = P, the equal but opposite thing. This means a = 0; so there is no acceleration inward or outward along the string. Which is why the top m stays at distance R from the center of rotation.

Bottom line...centripetal force always, without exception, points inward toward the center of rotation. And, there is always an equal but opposite faux force, called centrifugal force, when the mass m is at a fixed distance from the center of rotation.

Answer 3

I disagree with the first answer. The 2nd answer is basically correct. Centripetal simply means 'toward the center.'

There are cases where the path isn't a circle, and in those cases you need to locate the center of curvature of the portion of the path the particle is on.

Sometimes the centripetal force is easy to identify, like the tension force pulling inward on something going in a circle at the end of a rope, or the gravitational force on a body in a circular orbit.

A much more complicated problem would be to find the centripetal force on a projectile at various points along its parabolic path -- the center of curvature changes position as you go along the arc of the parabola.

Answer 4

It's the one that points inwards towards the center of the circle.