# Centripetal Motion and Force

*Something that makes the world go round*

Centripetal motion deals with the motion of an object traveling through a circular shape. Examples of this can be seen when a cart moves around on a Ferris wheel or even a satellite orbiting above earth. They all follow circular or elliptical paths. However, it is important to remember that the object does not have to travel in a full circle in order to have centripetal motion. Airplanes that make a turn and cars that travel across a curved road are both examples in which objects travel partial circles. However, the question still lies as to how these objects stay in a circular path. Centripetal motion tries to answer these questions.

**How does it stay in a circle?**

The objects stay in a circular path because of the concept of centripetal acceleration (CA). The object is constantly accelerating towards the middle of the circle, thus preventing the object from flying off the circular path. For example, imagine what would happen if, as you were twirling a ball on a string, the string broke. Would the ball continue to spin in a circle or would it fly off in a particular direction?

Naturally, the ball would fly off in a particular direction. This is its natural state. However, the string is keeping the ball moving in a circular motion, so the string is exerting a centripetal force that keeps the ball going in this circular motion. Any time there is a force, there is an acceleration, in this case a centripetal acceleration.

In physics, you’ll see this equation for centripetal acceleration written as:

Centripetal Acceleration (a_{c}) =v^{2}/r

Where v is the **tangential** velocity of the object and r is the radius of the circle as it travels around. Tangential velocity is the velocity at which the ball would "fly off" in the above example and is always tangent to the curve.

**What is centripetal force?**

As we mentioned above, any time there is an acceleration and a mass, there is a force because of Newton's second law. In this case, the force we are dealing with is called the Centripetal Force. The Centripetal Force is defined as F_{c}=ma_{c}, which is Newton’s Second Law, just applied to a circle. Knowing that centripetal acceleration is the tangential velocity squared divided by the radius (as mentioned above), expanding it gives us:

F=mv^{2}/r

Therefore, this force keeping an object with mass in a circular motion must have centripetal acceleration and is directed towards the middle. The magnitude of the force varies depending on the situation. In the ball with a string, the tension force in the string keeps the ball in place.

**Don’t get confused between force and acceleration**

Centripetal acceleration and centripetal force may seem like they’re the same thing, but they’re not. Centripetal acceleration explains the motion of the object in the circle while the centripetal force is the influence that keeps the object in the circle. As vectors, both are pointed towards the center, but one is a force vector and the other is an acceleration vector—two very different things.