Circular motion seems a very difficult concept to understand. It contradicts our everyday experience to deny that there is a force pushing us away from the center of a circular path. Entering a curve as we ride in a car, it seems quite clear to us that we are being shoved into the car door... or are we? Perhaps the door is shoved into us! Physics offers us a very different view here --one of a "noninertial reference frame"-- a frame that is accelerating.

The word "centripetal" means "center seeking" and physicists insist on using it to describe the sum of forces that create circular paths. What most people refer to as "centrifugal forces" (away from center) are nonexistent and are labeled "fictitious".

Centripetal force never acts to change the speed of an object but acts only to change the direction of the object. It always pushes perpendicular to the velocity of the object. So it is not a "tangential force"! It does NOT act along the circle but instead acts along a radius pointing to the center ALWAYS.

Such centripetal forces occur all around us... in atoms, in washing machines, on amusement park rides and in our solar system in planetary motion. As it turns out, the door of the car pushes us inward rather than pushing outward on us as we travel around a curve. We actually push outward on the door! (Action-reaction pair of forces) but the car pushes all passengers toward the center of the circular curve. Without the car, the object travels in a stright line path at constant motion.

                                                               

HINTS FOR WORKING WITH CIRCULAR MOTION

HINT 1

DON'T think of CENTRIPETAL FORCE as a separate force with an identity such as that of weight, friction, etc. It is merely the sum of ordinary physics forces acting to produce a circular path.

HINT 2

DON'T create and label a vector for centripetal force on a force diagram. Centripetal force describes a NET force NOT an individual force. IFand ONLY IF there is just a single force acting then that single force becomes the centripetal force only because it equals the net force.

HINT 3

DON'T confuse CENTRIFUGAL force, a very misused term, with INERTIA. It is rare to experience a force that pushes away from the center of the circular path (though normal forces do at times). Most of the time, what is termed centrifugal force is just the tendency to travel in a straight line path (Inertia).

HINT 4

DO draw a force diagram and clearly label all the forces acting.

HINT 5

DO use a = v^2 / R in F net = ma as the net acceleration of any object that travels in a circular path.

CIRCULAR MOTION LINKS

CIRCULAR MOTION AT CONSTANT SPEED

Steps for Derivation of Centripetal Acceleration Equation: a = V^2/ R

1) aaverage = D V/ D t = (V 2 - V1)/ D t

(This is one of the basic five kinematics equations!)

The diagram at left shows the path, the radius vectors, and the velocity vectors along the path. The speed or magnitude of the vector does not change but the direction does!

Figure 2

2) Since the triangles in figures 2 & 3 are similar (SAS), then  V/ R = D V/ D R.   note:       V1 = V2 = V

3) So D V = D R (V/R)

Figure 3

4) a = [D R ( V/R)] / D t

5) a average = [D R/D t] (V/R)      (regrouping)

This equation will always be used for the net force, F net = ma, when an object travels in a circular path at constant speed!

6) a instantaneous = lim [D R/D t] (V/R)                                 D t ® 0

7) a instantaneous = V(V/R) = V^2 / R