How To Find Normal Force In Circular Motion: Several Approaches and Problem Examples

In this article, we will talk about how to find normal force in circular motion. Continue reading this article. 

Even in a circular motion, the normal force normally acts, i.e., perpendicularly to the moving object. There are different formulas for different cases to find normal force. Let us look at several approaches and problems to understand how to find normal force in circular motion.  

When a body moves on the circumference of a circle, i.e., on the circular path, the motion is said to be circular motion. It can be uniform when the angular velocity is constant all the over journey or can be non-uniform when the velocity keeps changing. 

To understand the circular, take the example of your ceiling fan. The blades of the fan move on a circular path about the central point. Some other examples are the Ferris Wheel, rotation of Earth, and many others. 

The bodies moving on a circular path, the force that exerts on it is called centripetal force. In physics, it is the resultant force that acts on a body moving on a circular path. The direction of this force is always towards the center. 

What is the normal force of an object in a circular motion?

For any object, whether in a circular motion or linear motion, the two forces are sure to act on it; gravitational force and normal force (if it is in contact with the surface). And thus, for a circular motion also, there is a normal force. 

We know how to find the normal force with coefficient of friction. Now we need to know how to find the normal force in a circular motion. 

Now two things that we need to know before starting is that centripetal force is the sum of normal force and weight. And the next thing that always acts towards the center. We have the formula of centripetal force as: 


How to find normal force in circular motion

Now the above figure shows an object moving in a circular path starting from point B. At point B, we can see that the weight, W, is acting downward. The normal force, N is acting perpendicularly to the object, and centripetal force, F, is acting towards the center. Now we have:

How to find normal force in circular motion

Now the particles move to point A. Here we can see that both centripetal force and a normal force acts in the same direction, whereas weight acts downwards. So, we have 

How do you find the normal force on a loop?

A loop like a roller coaster or Ferris wheel is an example of circular motion. At every point of circular motion, two forces are acting: Gravitational force to pull the object downwards and Normal force in an upward direction to keep the object moving on the rail. 

Now, what happens is, at the top of the loop is if there is no rail, the object would continue moving in the same direction (upward) for some time. But as there is gravity acting on the object, it pulls it down, so the object changes its direction and moves on a curved path. This happens at every turn, and therefore the object moves on a loop in a circular motion. 

Now at the top of the loop, the normal force would be:


And at the bottom of the loop, the normal force will be: 


So, that was all about how to find normal force in circular motion. Now let us look at some problem examples.

Problems on How to Find Normal Force in a Circular Motion

Calculate normal force acting on an object 5 kg moving at the velocity of 10 ms-1 at the bottom of the loop. The radius of the loop is 2 m. 

Solution: We are given: 

m = 5 kg

r = 2 m

v = 10 ms-1

Therefore the normal force is:



N = 300 newtons

Calculate the normal force exerted on a driver of a car at the top of the circular hill. The car is moving with a velocity of 9 m/s, and the mass of the driver is 70 kg. The radius of the circular hill is 100 m.  

Solution: We are given:

m = 70 kg

r = 100 m

v = 9 ms-1

Therefore the normal force is:

Frequently Asked Questions (FAQs)

Explain circular motion with examples.

In a circular motion, the body moves along the circular curves. 

Ferris Wheel is a basic example of circular motion. It moves on a fixed circular path along with a fixed point. Some other examples of circular motion are satellites revolving around Earth. 

What is centripetal force?

Centripetal force is the total force that emerges during circular motion. 

Without centripetal force, the body won’t be able to move on the circular curves; it will continue moving in the same direction. The centripetal force always acts towards the center and along the radius. 

How to find normal force in circular motion?

The weight component and the normal force together constitute the centripetal force.    

For any object moving on a circular path, the normal force does not remain the same. On the top of the circular path, the normal force is given by the formula: 


The normal force on the bottom of the circular path is:


Is normal force the same as a centripetal force? 

No, it is not necessary that normal force is always equal to the centripetal force of the object. It usually depends on the position of the object on the curve. 

Rabiya Khalid

Hi,  I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: In my free time, I let out my creative side on a canvas. You can check my paintings at:

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