You may use whichever expression for centripetal force is more convenient.

The first expression is in terms of tangential speed, the second is in terms of angular speed: F c = m v 2 r F c = m v 2 r and F c = m r ω 2 F c = m r ω 2.īoth forms of the equation depend on mass, velocity, and the radius of the circular path. Therefore, the magnitude of centripetal force, F c, is F c = m a c F c = m a c.īy using the two different forms of the equation for the magnitude of centripetal acceleration, a c = v 2 / r a c = v 2 / r and a c = r ω 2 a c = r ω 2, we get two expressions involving the magnitude of the centripetal force F c. For uniform circular motion, the acceleration is centripetal acceleration: a = a c. According to Newton’s second law of motion, a net force causes the acceleration of mass according to F net = m a. The direction of a centripetal force is toward the center of rotation, the same as for centripetal acceleration. Just a few examples are the tension in the rope on a tether ball, the force of Earth’s gravity on the Moon, the friction between a road and the tires of a car as it goes around a curve, or the normal force of a roller coaster track on the cart during a loop-the-loop.Īny net force causing uniform circular motion is called a centripetal force. We call the acceleration of an object moving in uniform circular motion the centripetal acceleration a c because centripetal means center seeking.īecause an object in uniform circular motion undergoes constant acceleration (by changing direction), we know from Newton’s second law of motion that there must be a constant net external force acting on the object.Īny force or combination of forces can cause a centripetal acceleration. If we imagine Δ s Δ s becoming smaller and smaller, then the acceleration would point exactly toward the center of rotation, but this case is hard to draw. (The center of rotation is at the center of the circular path). Acceleration is in the direction of the change in velocity in this case it points roughly toward the center of rotation. The direction of the instantaneous tangential velocity is shown at two points along the path. The sharper the curve and the greater your speed, the more noticeable this effect becomes.įigure 6.7 shows an object moving in a circular path at constant speed. This fictitious force is known as the centrifugal force. Inside the car it appears as if you are forced away from the center of the turn. This isn’t an actual force that is acting on you-it only happens because your body wants to continue moving in a straight line (as per Newton’s first law) whereas the car is turning off this straight-line path. What you notice is a feeling of sliding (or being flung, depending on the speed) away from the center of the turn. If you hold the steering wheel steady during the turn and move at a constant speed, you are executing uniform circular motion.

You experience this acceleration yourself every time you ride in a car while it turns a corner. Therefore, an object undergoing uniform circular motion is always accelerating, even though the magnitude of its velocity is constant. We know from kinematics that acceleration is a change in velocity, either in magnitude or in direction or both.

Note that, unlike speed, the linear velocity of an object in circular motion is constantly changing because it is always changing direction. The simplest case of circular motion is uniform circular motion, where an object travels a circular path at a constant speed. In the previous section, we defined circular motion.

Uniform circular motion