The Centripetal and Centrifugal Pair

Introduction

Being an 11th grade science student, I understand how taxing and confusing physics can be. I still remember studying the 1st chapter of 9th grade physics. That one concept annoyed me for hours. I did what not to understand it: googled, asked my parents, read through the same lines multiple times and then gave up. Finally, I understood it with the help of my cousin and their explanation made it seem so easy that I remember it even today. 

I guess the highs and lows in physics make it fun as well as hard to learn but if you put in some effort and get the right guidance, you’re sorted. I got lucky that way and have been doing well.

So, this blog is for those who won’t leave a concept till they get every part of it, who have a love-hate relationship with physics or those who are just curious about everyday life. I hope to help my readers learn and like physics just a bit more.

I always found the pair of centripetal and centrifugal forces fascinating. They are so similar yet so different. Both act on a body in circular motion but in opposite directions. Both have observable effects but only one is real. Centripetal might be easy to understand but centrifugal might give you a hard time. These concepts might not be tested that often but they do have some relevant applications in real life and are helpful in later classes. So, let’s start…

Centripetal Force

Centripetal force is the force that acts on a body in uniform circular motion in a direction towards the centre of the circular path (as shown in the figure by F). It is not a new force but an accompanying force to circular motion, usually provided by gravity or a string. Why is the force needed, why does it act towards the centre and where does it come into play? Find your answers here. 

When a body moves in a circular path with a constant speed, it’s said to be in uniform circular motion but it has a variable velocity. This is because the body’s direction of motion at each point of the path constantly changes (as shown in the figure by v). According to Newton's first law of motion, there must be a force to change the direction of the body. It says that a body will move with uniform speed in a straight line unless a force acts on it. For circular motion, that direction changing force is centripetal force.

Now, if this force were to act in any other direction it would change the speed and disrupt uniform circular motion. For instance, if it acts in the direction of the velocity, the force will increase the speed. If it acts in the direction opposite to velocity, the force will decrease the speed which is not possible as speed needs to be constant. 

Centripetal force can be seen in our everyday life. When a string with a ball tied to one end is rotated, the centripetal force is provided by the tension (force in string when stretched). If we rotate too fast, the string breaks and now can’t provide the centripetal force for circular motion so the ball flies off in a straight line. 

The motion of the moon around the earth is uniform circular motion for which the centripetal force is provided by the force of gravity of the earth. Without it, the moon's motion would be in a straight line.  

In an atom, the electrons revolving around the nucleus are in uniform circular motion for which the centripetal force is provided by the electrostatic force of attraction between the negatively charged electrons and positively charged nucleus. 

Another really cool example - the well of death. A bike can move horizontally on a vertical wall due to many forces, one of which is centripetal force. This is provided by the normal reaction force of the wall, which is exerted by the wall as  a reaction to the force it experiences due to the bike. It keeps the bike in circular motion. The frictional (between tires and wall) and gravitational forces (weight of the bike) balance each other and keep the bike from falling.

Centrifugal Force

Centrifugal force is the force that acts on a body in a direction away from the center of the circular path. It is equal in magnitude but opposite in direction to centripetal force. Here, we cannot apply Newton’s third law and say that centripetal force is the force of action and centrifugal force is its force of reaction just because they are equal and opposite. This is because the forces of action and reaction don’t act on the same body. A swimmer pushing the water with their arms (action force on water) and the water pushing the swimmer back (reaction force on swimmer) can be an action reaction pair. Also, centrifugal force is not a real force so it can’t be a reaction force. If it’s not real, what is the point of it? Let’s see with an experiment.

The experiment involves a merry-go-round with a string tied to its center. On the other end of the string a ball is attached. When the merry-go-round is stationary, the string is loose and the ball is stationary on the platform. As the merry-go-round starts rotating, the string gets stretched, the force of tension acts and makes it tight. Now the ball’s in the air and its motion is to be studied from 2 points of view: of a person standing outside the merry-go-round and of a person standing at the center of the merry-go-round at the point where the ball is attached.

The person outside the merry-go-round observes the ball moving in a circular path (along the green line). According to this person, the tension in the string provides the necessary centripetal force for circular motion. 

The person standing at the center of the merry-go-round observes the ball stationary in front of him. This is because as the ball moves, the person’s position also changes in line with the ball (1-a, 2-b, 3-c, 4-d). According to this person, along with the centripetal force an equal and opposite force acts on the body such that the net force on the body is zero and it is stationary in front of him. This force is the centrifugal force on the string. 

So, centrifugal force is not a real force as we don’t know what causes it (unlike how we know the cause - tension in string - for centripetal force ) yet we considered it to describe the observations of the person on the merry-go-round (who had these observations as he was rotating). It is thus called a fictitious force. 

When we are in a vehicle that takes a sharp turn towards the right, it travels in a circular-type path. We instantly feel pushed to the left in a direction away from the centre of the circle, but really there is nothing that's exerting an outward force on us. This fictitious force is centrifugal force.

This feeling can be explained by inertia: the property of a body to resist change in direction, state of motion or rest . Our feet in contact with the vehicle's body move with it towards the right but  our upper body moving in a straight line tends to continue the same motion in the same direction, making us feel pushed towards the left. 

Centripetal and centrifugal forces are equal, opposite and play an important role in understanding circular motion. That’s the basics of the centripetal and centrifugal pair for you. 

Check your understanding with this quick question-:

Q. While driving on a rainy day, a person tries to make a left turn but the car continues in a straight line. What caused this phenomenon?

Hint: Was it an outward force or lack of an inward force? 

The answer will be revealed in the next blog...