Motion in a Vertical Circle

A body is said to be in circular motion when the body moves at a definite distance from a fixed point along a circular path. The fixed point acts as the centre and the fixed distance acts as the radius of the circular path that the body is travelling.

A body undergoing circular motion constantly changes its direction of movement, which is tangential to the circular path at that point. For any body performing a circular motion, centripetal force is a must, which acts along the radius towards the centre.

This force that provides the acceleration to the body is expressed as,

Fc(Centripetal force) = mv2R

Here m is the mass of the object, v is the linear velocity of the particle and R is the radius of the circular path.

Terminologies used in the study of circular motion

• Distance (d): Distance is the measurement of the actual path travelled by the body from the initial point to the final. Distance is a scalar quantity (i.e. it only has magnitude). The distance is represented in ‘m’ (metres) in the SI representation system. 

• Displacement (s): Displacement is the shortest path between the initial and final points travelled by the body. Unlike distance, displacement is a vector quantity, which means it has both magnitude and direction. The SI unit is the same as distance, i.e. ‘m’.

• Speed (v): Speed is defined as the rate of change of distance concerning time. In other words, speed is the ratio of distance travelled by the body in a particular time interval.

Speed = DistanceTime

The SI unit of speed is ‘m/s.’ It is a scalar quantity.

• Velocity (v): Velocity is defined as the rate of change of displacement concerning time. It is the ratio of displacement (shortest distance) and time. Velocity is a vector quantity.

Velocity = DisplacementTime

The SI unit of velocity is ‘m/s’.

• Acceleration (a): Acceleration is the rate of change of velocity concerning time, which means the ratio of change in the velocity of the body per unit time. It is also a vector unit.

Acceleration = VelocityTime

The SI unit of acceleration is ‘m/s2’.

• Force (F): Force can be defined as the physical quantity which, when applied to a body, tends to change its state of rest or state of motion. On the application of force, if the body is at rest, it will start moving in the direction of the applied force. It is a vector quantity.

Force= m × a (mass × acceleration)

The SI unit of force is ‘N’ (Newton).

• Momentum (P): The momentum of a body is the product of its mass and the velocity at which it moves. The body’s momentum is directly proportional to the mass and speed of the body. Momentum is a vector quantity.

Momentum = m x v (Mass x Velocity)

The SI unit of Momentum is ‘Kg m/s.’

Motion in a Vertical Circle

Gravity must be considered while analyzing the motion of a body in a vertical circle. Because of the action of the Earth’s gravitational field, the magnitudes of the body’s velocity and strand pressure keep on changing constantly. It is greatest at the lowest point and least at the highest position. As a result, the vertical circle’s motion is not a uniform circular motion.

Now, we have a basic understanding of circular motion. The distance of the material remaining unchanged from a fixed plane in a circular motion is known as well. Circular motion is classified into two types: uniform circular motion and non-uniform circular motion. When a ball is tied securely to a cord, it will move in a circle. This happens because of circular motion. Circular motion is also demonstrated by an automobile that is turning in a curve.

Circular Motion in a vertical plane

Suppose a body with mass ‘m’ is connected to the end of a string and spun in a vertical circle with radius ‘r’. Let ‘v1’ and ‘v2’ be the body’s velocities, and ‘T1’ and ‘T2’ be the tensions in the string at the lowest point A and highest point B, respectively. 

As illustrated in the picture, the velocities of the body at locations A and B will be oriented along tangents to the circular route at these places. In contrast, tensions in the string will always act in the direction of the fixed point O. At the lowest point A, a portion of tension T balances the body’s weight, while the remainder produces the necessary centripetal force. Therefore,

T1-mg=mv12/r

The tension in the string and the person’s weight generate the required centripetal force at the highest point.

T2+mg=mv22/r

Conclusion

Technological advances have resulted in a re-evaluation of subjects appropriate for consideration in introductory physics courses. We no longer have to limit ourselves to systems that can be explained using simple, well-behaved mathematical models. Multimodal approaches, simulation software and computer algebra packages have permitted us to tackle challenges that were unthinkable merely two decades ago.

Circular motion on a vertical plane involves a wide range of movements, with the centripetal acceleration pointing in any direction amongst up, horizontal and down and the force from the ride mixing with gravity in a constantly changing manner. The various ride examples demonstrate that the moving body may spin along multiple axes, or not at all. They seek to raise the consciousness of the body’s posture, forces and rotation along various axes.