Centripetal Force

The term Centripetal Force is used in mathematics and physics to define the influence that causes a single unit of an object to experience a change in speed and direction for the purpose of following a curved pathway. The direction of the centripetal force is perpendicular to the object's velocity at the immediate osculating circle of the curved pathway. The term centripetal is coined by combining two Latin words - centrum (meaning center) and petere (meaning tendency towards). The combination of both these terms conjures up the implication that it is a force that is aimed towards the central portion of the inner side of the angle of the pathway's curvature. Let's take a detailed look at the meaning and definition of centripetal force before proceeding towards how to measure it.

What is Centripetal Force

To put it in the words of Sir Isaac Newton, "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center." To put it in a layman's parlance, centripetal force is that type of force which compels an object to move along a curved or circular path, without getting stationed at the point of curvature after coming along a straight path. It is this force that keeps planets moving along an elliptical path around the sun and the theory of centripetal force explains the mechanism behind the functioning of roller coasters and giant wheels at amusement parks. Now that we have got to the basics, another question arises - where does the centripetal force come from? The answer is gravity.

We all know that gravity causes objects to get attracted towards each other. In case of centripetal force, this same force of gravity establishes an attraction in the mean location of the mass of an object towards the mass center of the mass of another object in such a way that the mobile object advances towards the stationary object until the mean location of each object is closest to the mean location of the other. Once this happens, the force of gravity starts to weaken its hold, causing the movable object to start moving away from the point of curvature to once again follow a subsequent straight path. When this process if repeated, we can see a movable object going round and round along a circular or elliptical path.

Centripetal Force Formula

Now that we've understood the basics of centripetal force, let's take a look at how it can be mathematically calculated. The various components of a typical centripetal force equation consists of the following:-

• mass of the moving object
• speed at which the object is moving
• radius of curvature of the pathway

Using all these components to form an equation, the formula of centripetal force goes as follows:-

F = ma_c = mv² / r

where:

• F = Centripetal force
• m = mass of moving object
• a_c = Centripetal acceleration
• v = Speed at which the object m is moving along the pathway
• r = Radius of curvature

Centripetal Force: Two Perspectives

With regards to movement along a curved pathway, the theory of centripetal force applies to two different scenarios of an object moving along a curved path. These two situations can be put down as follows:

Uniform Circular Motion - Where the moving object moves along a regular circular or elliptical path at a fixed or consistent rate of rotation.

Non Uniform Circular Motion - Where the object moves along a circular pathway at an irregular rate of rotation, causing the object to form tangents with the curvature of the pathway at times.

In case of the first instance, the vector of velocity and the vector of position are always perpendicular to each other. Therefore, as the position changes in a circular motion, the corresponding perpendicular velocity also does the same. Owing to this tandem of motion, the uniformity of the rate of rotation is maintained. In case of the second instance, the position and velocity vectors are not at perpendicular angles to each other. Therefore, there is no tandem in the change of position to the change of speed, causing the rate of rotation to become irregular. This results in the object touching the pathway at some points during its closest stints towards the point of curvature.

That was a brief overview of centripetal force. This is a theory of physics that applies mathematical tools to arrive at a figure of measurement of the force. Hope the above explanation helped you understand the basic concept of centripetal force without confusing you further with complicated mathematical notations and physics terms. All the best for that oncoming physics test (if you're expecting one)!