Circular Motion

Introduction

Circular motion is a motion in which a body travels a definite distance along a circular path. Let’s learn about the meaning of motion, circular motion, the types of circular motion, its properties, and how to derive a velocity of a body performing the circular motion. 

What is motion?

Motion can be defined as any object or body changing its position in its surroundings concerning time. When an object is moved from its initial position in a particular interval of time, it is said to be under motion.

Motion is a very common concept that we come across in day-to-day life. It can be said that every component of the universe performs some form of motion. Some examples can be cars moving on the road, boats sailing in the ocean, birds flying in the sky, and the earth moving around the sun. All these bodies can be said to be performing a motion.

Terminologies used in the study of Circular motion

• Distance (d): Distance is the measurement of the actual path travelled by the object/body from the initial point to another. Distance is a scalar quantity (i.e., only 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 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 object/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 (v) = 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 object/body per unit time. It is also a vector unit.

            Acceleration (a) =  VelocityTime

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

• Force (F): Force can be defined as the physical quantity which, when applied to an object/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 x a (mass x acceleration)

            The SI unit of force is ‘N’ (Newton).

• Momentum: The momentum of a body is the product of its mass and the velocity with which it is moving. The body’s momentum is directly proportional to the mass and speed of the object/body. Momentum is a vector quantity.

            Momentum (P) = m x v (Mass x Velocity)

            The SI unit of Momentum is ‘Kg m/s.’

What is Circular Motion?

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 the body is travelling.

A body performing Circular Motion constantly changes its direction of movement, which is tangent 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 providing the acceleration to the object/body is,

Fc(Centripetal force) = mv2R

Here m is mass of object

v is the linear velocity of particle

R is radius of circular path

Circular Motion Examples

The motion of a car on a level road:

Let us assume a car is moving on a level road, with mass ‘m’ and ‘g’ as the acceleration due to gravity acting upon it.

When the car is taking a turn on the road, a total of three forces act simultaneously on the car:

1. The weight of the car, mg
2. Normal reaction, N (Acting perpendicular to the ground in the opposite direction)
3. Frictional Force between the wheels of car and road, f.

The car is moving in the horizontal plane, so there is no vertical movement which means there is no acceleration in the vertical direction (Along X-Axis).

Therefore,

    N – mg = 0

        N = mg (i)

When a car moves along the curved road, centripetal force is required to perform this circular motion. This centripetal force is provided by the frictional force (f) between the wheels of the car and the surface of the road.

Since the centripetal acceleration is only produced in the case of static friction, and as we know, static friction opposes the motion.

According to this analogy,

f = mv2R  μsN

∴ v2 μsNRm= μsRg (N=mg)

∴ v = μsRg

We can conclude that velocity is independent of the car’s mass according to this derived equation.

Types of Circular Motion

Based on the direction and rate of rotation of the body, Circular Motion can be further subdivided into two types:

• Uniform Circular Motion

• Non-Uniform Circular Motion

When the rate of rotation of the object/body remains constant concerning time, it is said to be performing Uniform Circular Motion. In other words, the speed of rotation remains constant along the circular path. For every object performing Circular Motion, some acceleration is provided by the centripetal force, which acts along the path of radius towards the centre. Hence, the acceleration is perpendicular to the direction of velocity at every point of motion. 

When the rate of rotation of the object/body changes concerning time, it is said to be performing Non-Uniform Circular Motion. The speed of the rotation changes at every point in the circular path.

Characteristics of the body performing Uniform Circular Motion

• The speed of the object/body remains constant along the circular path.
• The velocity of the object/body changes concerning time.
• The body carries uniform acceleration.
• It does not possess tangential acceleration.

Components in Uniform Circular Motion

• Angular Displacement: The angle by which the object moves with the centre is called Angular Displacement.

Angular Displacement (Δθ) =ΔSR

• Angular Velocity: The rate of angular displacement per unit angle of a body performing Uniform Circular Motion.

Angular Velocity (Δω) = Δθt

• Angular Acceleration: The rate of change of angular velocity per unit angle is Angular Acceleration.

Angular Acceleration (Δ) = Δωt

Let us see a few Uniform Circular Motion examples.

• Earth revolving around the Sun.
• Electrons revolve around the nucleus of an atom.
• The motion of the hands of a clock.

Hope this gives you an understanding of circular motion, its properties, and various terms related to it.