Real-Life Applications of Circular Motion in Physics
In Physics, the concept of circular motion has multiple usages. Once understood the concept is applied to solve the problems of rotation. Understanding the importance of the topic we have compiled a separate article explaining the concept of circular motion.
In this particular article, we shall focus on understanding the dynamics of circular motion. The explanation will focus mainly on the following concepts-
Table of Content -
Circular motion - introduction with example
What is the Dynamics of a circular motion
Right-hand rule
Dynamics of a Uniform circular motion
Dynamics of a Non-uniform circular motion
FAQs
What is Circular Motion?
A body moving along the circumference of the circle with a constant speed is said to be exhibiting a circular motion.
For example, a car has a circular motion with a speed of 8 m/s along the circumference of 24 meters.
At a uniform speed, it will complete one cycle in 3 seconds.
It means in every circle, around the 24 m circumference of the circle, a body would take the same time of 4 seconds.
So, this relationship between the circumference of a circle, the time to complete one revolution, and the speed of the body can be described in terms of average speed.
So, Average speed = distance/time = circumference/time = 2 * π * r/T
As circumference = 2 * π * r
Dynamics of Circular Motion
Consider a body, moving along the circular path of radius r, in a clockwise direction in the plane of a paper.
Let's say the axis of the circular motion is passing through the center O, perpendicular to the plane of a paper.
As you see in Figure.1 below:
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The angle traced from P to Q is called the angular displacement, given by,
Ө = PQ/r = S/r
It is a vector quantity.
Its direction can be given by the right-hand rule.
Right-Hand Rule
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It states that if the fingers are curled in the direction of motion as if they are gripping the axis of rotation. The thumb that is held perpendicular to the curvature of the fingers represents the direction of the angular displacement vector.
As it exhibits a circular motion, it has a velocity too, and that velocity is the angular velocity.
Angular velocity is the rate of change of angular displacement. It is symbolized by ω.
Where ω = v/r
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It is a vector quantity.
By the right-hand rule, the thumb represents the direction of angular velocity.
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For a body having anticlockwise rotation, by the right-hand rule, the direction of ω is along the axis of a circular path and directed upwards, while for clockwise rotation, ω is directed downwards.
Dynamics of Uniform Circular Motion
The natural tendency of the body is to move uniformly in a straight line.
When we apply a centripetal force to it, it is forced to move along the circle.
Let’s consider a body, uniformly moving along the circumference of the circle when a pseudo-force is applied to it.
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The pseudo-force that acts along the radius and is directed towards the center of the circle is called the centripetal force.
According to Newton’s first law of motion , the body cannot change its direction of motion, an external force is required to maintain its circular motion.
However, this body continuously changes its direction of motion by itself, and there is a change in the velocity as well, that’s why it undergoes acceleration, called the radial centripetal acceleration.
a = v2/r
We know that F = ma
F = mv2/r
Dynamic of Uniform Circular Motion
While moving along the circle, the body has a constant tendency to regain its natural linear path. The tendency gives rise to a centrifugal force.
We can consider the centripetal force as the reaction of the centripetal force.
This means the centrifugal force is always equal and opposite to the centripetal force.
So, centrifugal force = mv2/r, and it acts along the radius, but away from the center of the circle.
The centripetal and the centrifugal forces are the forces of action and reaction, respectively.
Let’s say a stone is tied to one end of the string and the other end is rotated in a circle.
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As you can see in Figure.
When a centripetal force F1 is applied to the stone by the hand. It is pulled outward by centrifugal force, F2 acting on it because it tends to regain its natural linear motion.
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Dynamics of Non-Uniform Circular Motion
Consider a body moving with an angular velocity, ω.
It can change either its direction (clockwise or anticlockwise) or change its magnitude, while the axis of rotation remains fixed.
So, the position vector ‘r’ remains constant.
Since v = rω
Now, differentiating it with respect to time, we get,
dv/dt = ωdr/dt + rdω/dt
As a = dvdt, dr/dt = v, α (angular acceleration) = dω/dt
= vω + rα
a = ac + at
Here, ac = radial or centripetal acceleration, which is the measure of the rate of change of the velocity of the particle in the radial direction.
at = tangential acceleration, which is the measure of the rate of change of the magnitude of the velocity of the particle in the tangential direction.
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The magnitude of the resultant acceleration in the circular motion is given by,
a = |a| = √ac^2 + at ^2
Key Points from the Chapter -
Centrifugal and centripetal forces are equal in magnitude and are also opposite in direction.
Centripetal and centrifugal forces cannot be termed as action and reaction since action and reaction never act on the same body.
To complete the motion in a vertical circle is the basic requirement for a body under limited conditions.
For example, the stress on the string must not vanish before it reaches the highest point.If the stress vanishes earlier, it will be devoid of the necessary centripetal force required to keep the body moving in a circle.
Centrifugal force is known as the fictitious force which acts on a body, rotating with a uniform velocity in a circle and along with the radius away from the center.
FAQs on Dynamics of Circular Motion Explained: Key Concepts & Examples
1. What exactly is meant by the 'dynamics' of circular motion?
The dynamics of circular motion is the study of the forces that cause an object to move in a circular path. While kinematics describes the motion itself (like speed and acceleration), dynamics focuses on the 'why' behind the motion, primarily dealing with centripetal force as the cause for the constant change in direction.
2. How can you differentiate between uniform and non-uniform circular motion?
The key difference lies in speed. In uniform circular motion, the object moves at a constant speed, though its velocity continuously changes due to changing direction. In non-uniform circular motion, the speed of the object also changes, meaning it has both centripetal (radial) and tangential acceleration. For example, a planet orbiting the sun is nearly uniform, while a car speeding up on a curved track is non-uniform.
3. What is centripetal force, and why is it necessary for circular motion?
Centripetal force is the net force that acts on an object to keep it moving in a circular path, always directed towards the centre of the circle. It is not a new, fundamental force but rather the net result of other forces like tension, gravity, or friction. Without this inward force, an object would, according to Newton's first law, continue moving in a straight line tangent to the circle.
4. What are some real-world examples of forces providing centripetal force?
Centripetal force is provided by different fundamental forces in various scenarios. Here are a few examples:
- When a stone is whirled on a string, the tension in the string provides the centripetal force.
- For a satellite orbiting the Earth, the gravitational force between the Earth and the satellite acts as the centripetal force.
- When a car turns on a level road, the force of static friction between the tyres and the road provides the centripetal force.
5. If a car is turning on a flat road, what force prevents it from skidding outwards?
The force that prevents a car from skidding outwards while turning on a flat, level road is static friction. This frictional force between the car's tyres and the road surface is directed towards the centre of the curve, providing the necessary centripetal force to make the turn. If the car's speed is too high, the required centripetal force may exceed the maximum available static friction, causing the car to skid.
6. Why are the outer edges of curved roads and railway tracks often raised or 'banked'?
Roads and tracks are banked to aid in turning safely at higher speeds. When a road is banked, the vehicle is tilted. This causes a component of the normal force (the force exerted by the surface on the vehicle) to be directed towards the centre of the curve. This component of the normal force helps provide the required centripetal force, reducing the reliance on friction alone and making the turn safer and more stable.
7. In uniform circular motion, what is the relationship between an object's velocity and its acceleration?
In uniform circular motion, an object's speed is constant, but its velocity is always changing because its direction is changing. The acceleration, known as centripetal acceleration, is always directed towards the centre of the circle. This means the acceleration vector is always perpendicular to the velocity vector (which is tangent to the circle). This perpendicular force changes the direction of the velocity without changing its magnitude (speed).
8. Is centrifugal force a real force? Explain why or why not.
No, centrifugal force is not a real force; it is an apparent or pseudo force. It is a concept used to describe the outward push one feels when in a rotating frame of reference. From an inertial (non-accelerating) frame of reference outside the rotating system, the only real force acting is the centripetal force, which pulls the object inward. The feeling of being pushed out is simply the object's inertia—its tendency to continue in a straight line.
9. Is any work done by the centripetal force during uniform circular motion?
No, in uniform circular motion, the work done by the centripetal force is always zero. Work is calculated as the product of force and the displacement in the direction of the force. Since the centripetal force always acts perpendicular (at a 90° angle) to the direction of the object's instantaneous displacement, the work done is zero. This is consistent with the fact that the object's speed and kinetic energy remain constant.
10. What are the most important formulas for the dynamics of circular motion as per the 2025-26 CBSE syllabus?
For the Class 11 CBSE syllabus for 2025-26, the key formulas for understanding the dynamics of circular motion are:
- Centripetal Acceleration (a_c): a_c = v²/r
- Centripetal Force (F_c): F_c = mv²/r
- Maximum safe speed on a level road: v_max = √(μ_s * g * r), where μ_s is the coefficient of static friction.
- Optimal speed on a banked road (frictionless): v_o = √(r * g * tanθ), where θ is the angle of banking.
