# Centripetal Force vs Centripetal Acceleration: Comparative Analysis

Centripetal force vs centripetal acceleration is the one related to a circular motion in general. They are the main reason for a body undergoing circular motion.

Motion can be categorized in several different aspects, and one such being is the circular motion. Velocity, acceleration and force are required to drive the body in motion be it linear or circular.

But one needs to know the difference between the linear motion and circular motion that drives the body at a particular direction. Hence centripetal force vs centripetal acceleration is a combination of quantities that aid in the motion of a body in the circular motion.

In this article we will be discussing the difference and similarities of centripetal force vs centripetal acceleration. Any system that is under motion will need a force that pushes the body to be in the same until and unless an external force is applied.

Centripetal force is the required force which helps the body to go around in circular paths. There exists normal force too in any motion of the system. This normal force also keeps the mass of the body intact.

The normal force provides a force to the system to go move in circular motion which is called as the centripetal force. The magnitude of the normal force in curvatures is different form the normal force that is presented in system that is in linear motion.

## Centripetal Force Insights

Now let us dive deep into the discussion as to how the centripetal force is been exerted on the body under motion and how centripetal acceleration aids to that motion as well.

Let us say a car is moving straight on road with normal force and acceleration. Now there is a curve to pass through and what will be the force and acceleration that aids in passing through the curves. If the direction changes there certainly will be a change in the value of magnitude.

The answer to this is simple, that is, when the car is in linear motion the force exerted on the car is considered to be normal. This exertion of normal force is given by the road on the surface of the car.

The normal for is responsible for the motion in curved are because it the one providing the centripetal force for that curved motion.  When the normal force provides another force to the car in order to move in circular path then that is called as the centripetal force.

Generally centripetal force is given by the static friction that’s aid in circular motion of an object. The normal force in the curved path is greater than the one in straight path. Here the magnitude will face so many changes in the values in order to change the direction.

## Centripetal Acceleration Insights

Before we discuss the centripetal acceleration we need to know about the velocity factor and what drives it to the acceleration part.

The velocity in curved path is required to drive the object further down the path. When the speed is altered there will surely be acceleration aiding the motion. Centripetal acceleration is the one which has so many other factors are been included.

Time period and frequency are been considered when we take into account of the centripetal acceleration. Frequency in a circular path is the number of revolutions made by the object and the time period one such revolution is given the reciprocal of frequency.

In any circular motion the distance or displacement is given by the circumference of that circular path. So we consider the radius and the velocity with which the object travels the circular path.

We can easily find the centripetal acceleration in order to determine the various factors of the circular motion. Centripetal acceleration is the velocity divided by the radius and when the velocity is doubled the centripetal force is quadrupled.

## Centripetal Force vs Centripetal Acceleration Formula

Centripetal force formula is given by the mass, velocity and the radius.

fc=  m v2 / r

Where fc = centripetal force; m=mass; v= velocity; r= radius.

We must be aware of the fact that this formula is something that is similar to the conventional formula of the force. This formula is similar to the one where Newton’s Second Law provides, a product of acceleration and mass.

The tangential acceleration that occurs in the curved path is also known sometimes as the centripetal acceleration. The formula for centripetal acceleration is given as,

ac= v2r

Where ac is the centripetal acceleration; v= velocity; r= radius.

In a circular path where a body moves with a particular velocity we take into consideration of the revolution that body makes in a particular period given. The frequency is nothing but the number revolutions made.

## What is the formula for centripetal acceleration in vector form?

The centripetal acceleration in vector formula is simply the conventional formula.

The formula is given as ac=v2r. Expanding this formula we get the result as ac=rω2. Here ω indicated the angular frequency as it gives the number of rotations made by the object in the circular motion. The circumference if the circular path gives the distance in order to calculate the centripetal acceleration from which we can derive the value for radius.

## When does centripetal component of acceleration arise in a system?

The centripetal component acceleration in a system arises when the velocity is changed.

Normally when the body travels in the circular path it will take different directions which in turn change the magnitude too. A vector quantity will have a magnitude value and direction value so does the velocity.

## What is centrifugal force?

Force that pulls away from centre is centrifugal force.

When any object is pulled from the center of its circular path by action of a force is called the centrifugal force. Hence this force pulls the body away from the center point in the curved path.

Keerthana Srikumar

Hi...I am Keerthana Srikumar, currently pursuing Ph.D. in Physics and my area of specialization is nano-science. I completed my Bachelor's and Master's from Stella Maris College and Loyola College respectively. I have a keen interest in exploring my research skills and also have the ability to explain Physics topics in a simpler manner. Apart from academics I love to spend my time in music and reading books. Let's connect through LinkedIn-https://www.linkedin.com/in/keerthana-s-91560920a/