Vertical Circular Motion Using String

Physics holds the key to explaining the inner workings of the world. From depicting the speed of your race car to understanding the rotating earth, physics has all explanations. There are different kinds of motion one would know through physics. One such is circular motion. 

Circular motion can be of two types: vertical and horizontal. Vertical circular motion takes on the vertical circular path. There are various explanations and implications for the motion across a vertical circular path. 

Knowing circular motion and vertical circular motion will indicate a better understanding of the other relevant concepts. The below information will highlight circular motion, vertical circular motion formulas, and vertical circular motion examples.

What is Circular Motion?

In simplest words, circular motion is the motion that takes place across the circumference of a circular body. 

As the object moves in a circular path, it goes through acceleration and centripetal force. Here, centripetal force is a force that makes the body move in a curved pattern. The force exerted moves the body towards the centre point of rotation.

Examples of circular motion include movement around the earth, movement of the top, vehicle moving around a circular road, etc.

Circular motion can be of two types: uniform circular motion and non-uniform circular motion. In a uniform circular motion, the body or the object moves across the circumference at a constant speed and acceleration. In a non-uniform circular motion, the body or the object moves across the circular path at different speeds and acceleration.

Apart from these classifications based on uniformity, circular motion can be vertical and horizontal. We can consider the vertical circular motion under the umbrella of non-uniform motion. The next section explains motion on a vertical circular path, known as vertical circular motion.

What is Vertical Circular Motion?

The vertical circular motion refers to the motion around a vertical circle. One can generally explain this motion across a vertical circular path as vertical circular motion in a string. 

There are various examples to understand the vertical circular motion. These are the movement of the roller coasters, the movement of water buckets, and vehicles on hilly paths.

There are various conditions to be adhered to and satisfied for the motion to occur across the vertical circular path. These conditions are:

• In a vertical circular motion, the body must admit to the centripetal force and clear out its obstructions. By doing so, it will be constant in the circle

• The object in the vertical circular motion must exhibit the criteria of conservation of energy.

• Further, we can identify a vertical circular motion when gravitational potential energy converts into kinetic energy.

• The mass in a vertical circular motion must have a movement towards the downfall.

• As the body’s mass moves down in a vertical circular motion, the velocity should contradict and increase.

• In a vertical circular motion, the condition of weightlessness can occur. Weightlessness, in this context, refers to the complete collapse of the body’s weight.

In a motion across a vertical circular path, the force of gravity plays an essential role. Here, we can assume the motion as non-uniform because the body keeps changing its velocity, speed, and acceleration in such movement. 

In the beginning, the continuous decrease in mass increases the velocity. It destabilised the speed and acceleration of movement across such a vertical circular path.

Vertical Circular Motion Using String

We can understand the vertical circular motion with the following depiction using the strings. Here is a detailed explanation of it.

For instance

You have a small object as ‘m’ adjoined to one end of a string such that it rotates in a vertical radius circle. 

The object’s acceleration rises because it descends the vertical circle and reduces because it ascends the vertical circle in this example. As a consequence, the object’s pace is continuously in a shift.

It reaches its maximum point at the lowest vertical circle and its minimum point at the top. As a consequence, the object now no longer passes circularly. The weight ‘mg’ constantly travels vertically downward, no matter where the particle’s position is on the circle.

Here is an image elucidation of the previous hypothetical consideration. Through the image, let ‘L’ be the vertical circle’s shortest point and ‘u’ be the velocity of an object at L. Let ‘v’ be the object’s velocity at any given point P on a vertical circle. Assume ‘h’ as the gap between the end P and end L.

By the law of conservation of energy: 

Energy at point P = Energy at point L

(½) m v2 + m g h = (½) m u2

v2 + 2 g h = u2

v2 = u2 – 2 g h

v = √(u2 – 2 g h)

The above is an equation for the object’s velocity at any given point in a vertical circle when moving across the vertical circular path. It formulates the vertical circular motion formula. This approach is how we calculate the vertical circular motion when used with the string. 

Apart from these vertical circular motion formulas, various other formulas solve the tension. This tension refers to the discrepancies occurring when the object moves in a vertical circular motion using the string.

Vertical circular motion lays a better understanding of complex movements and phenomena that govern the world’s workings.

Conclusion

The above information includes a brief account of how physics explains the world’s inner workings. There are various motions classified in physics, and circular motion is one such. Circular motion is the motion that takes place when the body is moving on a circular path. Circular motion can be uniform or non-uniform.

The vertical circular motion is non-uniform and occurs when the body travels through a vertical circular path. There are various conditions for a vertical circular motion to take place successfully.

Lastly, the above information elucidates how to calculate vertical circular motion using a string. We can understand the entire concept better with vertical circular motion examples. The example also highlights the vertical circular motion formulas.