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
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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.
FAQs on Visualising Circular Motion in Vertical Plane
1. What exactly is meant by motion in a vertical circle?
Motion in a vertical circle describes the movement of an object along a circular path in a vertical plane. Unlike uniform horizontal circular motion, the object's speed is not constant. This is because gravity either works against the motion (on the way up) or with the motion (on the way down), causing the speed and tension to change continuously.
2. Can you give some real-life examples of vertical circular motion?
Yes, vertical circular motion is seen in many common situations. Some popular examples include:
- A roller coaster going through a vertical loop.
- A giant wheel or Ferris wheel at an amusement park.
- Swinging a bucket of water overhead in a vertical circle without spilling it.
- A simple pendulum swinging with a large enough amplitude.
3. Why does an object need a minimum speed at the lowest point to complete a vertical loop?
An object needs a minimum speed at the bottom to ensure it has enough kinetic energy to reach the top of the loop and complete the circle. If the speed is too low, it won't be able to overcome gravity. The critical condition is to have just enough speed so that the string or track still provides some tension or normal force at the very highest point, preventing the object from falling out of the path.
4. How does the tension in the string change as an object moves in a vertical circle?
The tension in the string changes continuously. It is maximum at the lowest point because the string must support the object's weight and also provide the necessary centripetal force. The tension is minimum at the highest point because gravity helps in providing some of the centripetal force, so the string doesn't have to pull as hard.
5. What are the most important formulas for understanding vertical circular motion?
The key formulas for an object of mass 'm' attached to a string of length 'r' are:
- Minimum speed at the lowest point to complete the loop: v_bottom = √5gr
- Minimum speed at the highest point: v_top = √gr
- Tension at the bottom: T_bottom = 6mg (when moving with minimum speed)
- Tension at the top: T_top = 0 (at the critical minimum speed)
6. How is the principle of conservation of energy applied to motion in a vertical circle?
The principle of conservation of energy is fundamental here. As an object moves up the circle, its kinetic energy is converted into gravitational potential energy, causing it to slow down. As it moves down, its potential energy converts back into kinetic energy, making it speed up. The total mechanical energy (sum of kinetic and potential energy) remains constant throughout the motion, assuming there is no air resistance.
7. Under which chapter is vertical circular motion covered in the CBSE Class 11 Physics syllabus for 2025-26?
The topic of motion in a vertical circle is an important application of energy conservation and circular motion concepts. As per the CBSE Class 11 Physics syllabus for the 2025-26 session, it is covered in Chapter 6: Work, Energy and Power.
