Centripetal Force

An object moving in a circle is constantly changing direction, so it must have a net inward acceleration even if its speed stays the same. Using the circular-motion acceleration formula a = v^2/r and Newton’s second law F = ma gives F = mv^2/r, so the required inward force grows with mass and speed, and gets larger for tighter circles. The force is not a new kind of force; it is the net inward force provided by tension, gravity, friction, or another real interaction.

Use this formula whenever you need the inward net force for uniform circular motion, such as a satellite orbit, a car rounding a flat bend, or a mass on a rotating arm. It is especially useful when the speed and radius are known and you need to find the force the rope, track, or gravity must supply.

• Using the tangential speed with the wrong radius, or mixing up diameter and radius
• Forgetting to square the speed, since the force depends on v^2 not v
• Treating centripetal force as an extra force instead of the net inward force supplied by real forces