What is Circular Motion?
Circular motion is the motion of an object along a circular path. In circular motion, the object keeps changing its direction continuously. Even if its speed remains constant, its velocity changes because velocity depends on both speed and direction.
Common Examples:
- The blades of a fan rotate in circular motion.
- A spinning top rotates about its axis.
- A giant wheel rotates about its axis.
Uniform Circular Motion
Uniform circular motion is the motion of an object in a circular path with constant speed.
Even though the speed is constant, the velocity is not constant because the direction of motion changes at every point on the circular path.
For example, when a satellite moves around the Earth in a nearly circular orbit, it keeps changing direction continuously. This change in direction requires acceleration.
Angular Displacement
Angular displacement is the angle through which an object moves along a circular path.
It is usually measured in radians.
If an object moves from one point to another on a circular path, the angle swept by the radius is called angular displacement.
Formula:
where:
- θ = angular displacement
- s = arc length
- r= radius of the circular path
Angular Velocity
Angular velocity is the rate of change of angular displacement.
It tells us how fast an object is rotating or moving around a circular path.
Formula:
where:- ω = angular velocity
- θ = angular displacement
- t = time taken
The SI unit of angular velocity is radian per second.
Time Period and Frequency
The time period is the time taken by an object to complete one full revolution. It is represented by T.
Frequency is the number of revolutions completed in one second. It is represented by f.
Relation between Time Period and Frequency:
or
The SI unit of frequency is hertz.
Linear Speed in Circular Motion
In circular motion, the linear speed of an object is related to angular velocity and radius.
Formula:
v = rω
where:
- v = linear speed
- r = radius of circular path
- ω = angular velocity
This means that for the same angular velocity, an object farther from the centre has greater linear speed.
Centripetal Acceleration
In circular motion, the direction of velocity changes continuously. This change in velocity produces acceleration.
This acceleration is always directed towards the centre of the circle.
It is called centripetal acceleration.
Formula:
where:
- ac = centripetal acceleration
- v = linear speed
- r = radius of the circular path
It can also be written as:
Centripetal Force
For an object to move in a circular path, a force must act towards the centre of the circle. This force is called centripetal force.
Formula:
where:
- Fc = centripetal force
- m = mass of the object
- v = linear speed
- r = radius of the circular path
It can also be written as:
Centripetal force is not a new type of force. It is the name given to any force that acts towards the centre and keeps an object moving in a circular path.
Examples:
- In the motion of a stone tied to a string, tension provides centripetal force.
- In the motion of planets around the Sun, gravitational force provides centripetal force.
- In the motion of a car around a curve, friction provides centripetal force.
**Speed is Always Constant, Velocity Changes
In uniform circular motion,
- The speed remains constant.
- However, velocity changes continuously because the direction of motion keeps changing.
Therefore, uniform circular motion is an accelerated motion.
This is an important idea in physics.
Examples of Circular Motion
The examples of circular motion are:
- Stone Tied to a String
- Motion of Planets
- Motion of Satellites
- Vehicle Moving Around a Curve
- Rotating Fan Blades
1. Stone Tied to a String
When a stone tied to a string is whirled in a circle, the tension in the string acts towards the centre. This tension provides the centripetal force.
If the string breaks, the stone moves off tangentially in the direction of its velocity at that instant.
2. Motion of Planets
Planets move around the Sun due to the gravitational force of the Sun.
The gravitational force acts as the centripetal force required for orbital motion.
3. Motion of Satellites
Artificial satellites move around the Earth because Earth’s gravitational force provides the necessary centripetal force.
4. Vehicle Moving Around a Curve
When a vehicle moves around a curve, friction between the tyres and the road provides centripetal force.
If the road is slippery or the speed is too high, the vehicle may skid outward.
5. Rotating Fan Blades
Each point on a rotating fan blade moves in a circular path around the axis of rotation.
Applications of Circular Motion
Circular motion is used in many areas of science and technology. Some of those are:
- Designing roads and railway tracks on curves
- Understanding planetary and satellite motion
- Designing centrifuges
- Studying rotating machines
- Explaining motion in amusement park rides
- Understanding rotating fans, wheels, turbines, and gears
Circular Motion and Gravitation
Circular motion is closely connected with gravitation.
Planets and satellites move in curved paths because gravitational force acts towards the centre of motion.
For a satellite orbiting the Earth, Earth’s gravitational force provides the centripetal force required to keep the satellite in orbit.
This is why circular motion is important for understanding orbital motion, satellites, escape velocity, and planetary motion.
Read more about Gravitation…
Glossary of Key Terms
Recap of the Key Terms in Circular Motion
- Angular Displacement: The angle through which an object moves along a circular path.
- Angular Velocity: The rate of change of angular displacement.
- Centripetal Acceleration: Acceleration directed towards the centre of a circular path.
- Centripetal Force: The force directed towards the centre of a circle that keeps an object moving in a circular path.
- Circular Motion: Motion of an object along a circular path.
- Frequency: The number of revolutions completed in one second.
- Linear Speed: The speed of an object along the circular path.
- Radian: A unit used to measure angles.
- Radius: The distance from the centre of a circle to any point on the circle.
- Revolution: One complete movement around a circular path.
- Time Period: The time taken by an object to complete one full revolution.
- Uniform Circular Motion: Circular motion in which the speed of the object remains constant.
Questions and Answers
Recap the concepts you have learnt. Try to answer the questions. You can find the answer to any question by clicking on the icon.
What is circular motion?
Circular motion is the motion of an object along a circular path.
Example: A stone tied to a string and whirled in a circle performs circular motion.
What is uniform circular motion?
Uniform circular motion is circular motion in which the speed of the object remains constant.
However, the velocity changes continuously because the direction of motion changes.
Why is uniform circular motion accelerated motion?
Uniform circular motion is accelerated motion because the direction of velocity changes continuously.
Even though speed remains constant, velocity changes because velocity has both magnitude and direction.
What is centripetal acceleration?
Centripetal acceleration is the acceleration directed towards the centre of the circular path.
It is given by:
What is centripetal force?
Centripetal force is the force directed towards the centre of the circle that keeps an object moving in a circular path.
It is given by:
Is centripetal force a separate type of force?
No. Centripetal force is not a separate type of force.
It is the name given to any force that acts towards the centre and produces circular motion.
For example, tension, friction, or gravitational force can act as centripetal force.
What provides the centripetal force for planets moving around the Sun?
The gravitational force of the Sun provides the centripetal force for planets moving around the Sun.
What happens if the string breaks while a stone is being whirled in a circle?
If the string breaks, the centripetal force disappears.
The stone moves off along the tangent to the circular path at that point.
What is the relationship between linear speed and angular velocity?
The relationship between linear speed and angular velocity is:
v = rω
where:
- v = linear speed
- r = radius of circular path
- ω = angular velocity
Give two applications of circular motion.
Two applications of circular motion are:
- Motion of satellites around the Earth
- Design of curved roads and railway tracks