Visualising Circular Motion in Vertical Plane

What is Circular Motion?

We already have some notion about circular motion. The distance of the substance is unchanged from a fixed plane in a circular motion, is already there in our knowledge. The classification of circular motion is divided into two categories. They are uniform circular motion and non-uniform circular motion. If a ball is hung tightly to a cord, it will be moving in a circle. This is due to the circular motion. Curve turn-taking of a car is also an example of circular motion.

Our topic for today is a different type of motion, called vertical circular motion.


Vertical Circular Motion

If the motion of a particle is taking place in a vertical circle, the motion will be non-uniform. So it is classified as non-uniform circular motion. Vertical circular motion with the equation, velocity, and tension is described hereunder: 


Vertical Circular Motion Equation

If a substance is fixed to a cord and moved in a vertical circle as hereunder

(image will be uploaded soon)

Between X and Y, tension will balance out the weight. Therefore the thread will always be stretched. The required speed to come to Y can be ascertained through sustaining mechanical energy.

Ex( Energy at X)=1/2 mu2.


Vertical Circular Motion Velocity

As the morsel is just there at point Y, the velocity or speed at Y is zero.

Ey=mgR

If both are equal, then what we will have is, u=√2gR


If we are calculating the minimum velocity to reach the level Z, can we guess the Z will be zero? Our answer is not at all. The reason is, if the speed at z will be zero, then it will be challenging to maintain the weight. The thread will be loosened. So at Z, velocity has to be similar in importance to the force that acts on the circular moving morsel directed towards the centre. It will make the tension zero.

mv2/R=mg ---(1)

Ez=mg( 2R)+mv2/2

If we substitute the value of v, we will have

Ez=2.5mgR

If the value of Ex equates to the value of Ez, we will have

u=√5gR;

Once we have all the critical values, we can structure our cases.

Case i: u < √2gR;

The ball will swing back and forth in a regular rhythm. But it will fail to reach point Y.

Case ii: √2gR < u <√5gR

Somewhere the ball will lose its contact between Y and Z. It will now have a projectile motion.

Case iii: u > √5gR

The cord will remain taut, and it will finish the round.


If a ball is fixed to a rod and moved in a vertical circle, what will happen? The point of difference is the velocity can be zero at the upper portion. Because of the normal reaction, the rod is now able to stabilize the pressure at the point. We will solve the problem once again through a case study. The cases for a rod will be like:  

Case i: u < √2gR

The particle will swing, and it will not be able to come to the point Y

Case ii:√2gR < u < √4gR

The ball will move back and forth to cross point Y. But it will not come to point Z. 

Case iii: u >√4gR

The particle will finish the round.


Tension in Vertical Circular Motion 

The movement of a mass on a string in a vertical circle has several mechanical theories. The tension at the top level of the circle is Ttop= Newtons. At the bottom of the circle, the corresponding tension is Tbottom= Newtons.


Some Factors to Know

  • The tension in a string differs when a body is moving around the circle. It is highest at the lower portion of the circle and lowest at the upper part.

  • If the string is to break, it will be the lowest part of the way to support the body as well as take it out of the straight-line method.

  • The body wants to finalize the completion of a vertical circle with the string still depending on its mass.

  • To complete a vertical circular movement, it will be easier to conduct it with the help of a hard rod. It would be best if you tied the object at the end of it. Whereas it is a little tighter while attached to the end of a cord.

FAQ (Frequently Asked Questions)

Q: What are the Meanings of Acceleration and Net Force?

The proportion of disparity in a morsel's velocity implementing a spinning movement to a particular time is known as angular acceleration. The value of it changes according to the same manner as velocity. The acceleration increases more and more with considerable variations in speed. The character of the acceleration depends on the positive and negative exchanges in velocity.


The term acceleration and net force are interlinked with each other. If one took place, the other would happen eventually. Acceleration is the amount of variation of velocity (say linear velocity) of a substance going through a rectilinear way. The net force is the total amount of troops that took place on an object.


If you go by Newton’s first law, the variation in speed can never be in action unless any disturbance occurs from outside. It is none but a force that is responsible for the fluctuations of the velocity of the object. The frictional force and external force in total are the determiners of the direction accelerate or decelerate. This is due to net force going through the substance.

Q: Who Said all Objects Fall at the Same Rate? Discuss with his Experiment.

A: Galileo Galilei let a substance fall from a leaning tower. He told me about a simple kind of motion. He claimed that all objects, whether heavy or light, take the same time to fall. He established his theory of uniform acceleration. The rate of coming down is totally up to the angle of inclination. It does not concern the mass.


Equation: S=1/2gt2


( S = distance covered, t= time consumed, g= acceleration due to gravity)