- What is Angular Velocity?
- Angular Velocity Definition
- Units of Angular Velocity
- Angular Speed vs Angular Velocity
- Instantaneous and Average Angular Velocity
- Uniform Circular Motion and Angular Velocity
- Relation Between Angular and Linear Velocity
- Angular Displacement and Angular Velocity
- How to Calculate Angular Velocity
- Constant Angular Velocity
- Direction of Angular Velocity
- Applications of Angular Velocity
- Angular Velocity in Everyday Life
- Angular Velocity in Physics (Class 11 & Class 12)
- Summary Table of Key Concepts
- FAQs on Angular Velocity
Angular Velocity
By Swati Singh
|
Updated on 25 Apr 2025, 13:54 IST
What is Angular Velocity?
Angular velocity tells us how fast something is rotating. It shows how quickly an object moves around a circular path. In simple words, angular velocity means the rate at which an object turns or spins around a point.
If you have ever watched a fan or a spinning wheel, you’ve seen angular velocity in action.
Angular Velocity Definition
In physics, angular velocity is the rate of change of angular displacement with respect to time. It measures how fast an angle is changing when something rotates.
Mathematically:
Angular Velocity (ω) = Angular Displacement (θ) / Time (t)
ω = θ / t
Where:
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- ω (omega) = Angular velocity
- θ (theta) = Angular displacement in radians
- t = Time in seconds
Units of Angular Velocity
The most common unit of angular velocity is:
- Radian per second (rad/s)
Other units you may see:
- Degrees per second
- Revolutions per minute (RPM)
SI Unit:
- The SI unit of angular velocity is radian/second.
Angular Speed vs Angular Velocity
Many people confuse angular speed and angular velocity. Let’s clear that up.
| Term | Type | Describes |
| Angular Speed | Scalar | Only shows how fast an object rotates |
| Angular Velocity | Vector | Shows how fast and in which direction the object rotates |
So, angular velocity is a vector, meaning it has both magnitude and direction.
Instantaneous and Average Angular Velocity
Instantaneous angular velocity is the angular velocity at a specific moment in time.
Average angular velocity is calculated over a time interval.
Formula:
ω = (θ₂ - θ₁) / (t₂ - t₁)
Uniform Circular Motion and Angular Velocity
In uniform circular motion, the angular velocity stays the same throughout. This happens when an object moves around a circle at a constant speed.
Relation Between Angular and Linear Velocity
Linear velocity is the speed of something moving along a straight path, while angular velocity deals with circular paths.
The relationship is given by:
v = r × ω
Where:
- v = Linear velocity
- r = Radius of the circular path
- ω = Angular velocity
So, the larger the radius, the faster the object moves in a straight line, even if the angular speed stays the same.
So, angular velocity is how fast the angular displacement is happening.
How to Calculate Angular Velocity
Use the formula:
ω = θ / t
Example:
If a wheel rotates radians in 2 seconds, then:
ω = / 2 = rad/s
To convert RPM to rad/s:
ω = (2π × RPM) /
Constant Angular Velocity
When an object rotates at a steady rate, it has constant angular velocity. This often happens in motors, fans, or wheels turning without speeding up or slowing down.
Direction of Angular Velocity
Angular velocity is a vector. The direction is given by the right-hand rule:
- Curl your fingers in the direction of rotation.
- Your thumb points in the direction of the angular velocity.
Clockwise motion = negative direction
Counterclockwise motion = positive direction
Yes, angular velocity can be negative depending on the direction.
Applications of Angular Velocity
You can find angular velocity in:
- Ceiling fans
- Gyroscopes
- Rotating wheels and gears
- Satellite motion
- Planetary orbits
- CD/DVD players
- Car tires
Angular Velocity in Everyday Life
- The Earth has an angular velocity as it spins on its axis.
- A fidget spinner rotating in your hand shows angular velocity.
- Bicycle tires while riding.
- Washing machines during the spin cycle
Angular Velocity in Physics (Class 11 & Class 12)
In Class 11 and 12 Physics, angular velocity is a key topic in:
- Rotational motion
- Mechanics
- Kinematics of circular motion
Students learn how angular velocity connects to torque, acceleration, and moment of inertia.
Summary Table of Key Concepts
| Concept | Details |
| Definition | Rate of change of angular displacement |
| Formula | ω = θ / t |
| SI Unit | Radian per second (rad/s) |
| Type | Vector quantity |
| Direction | Right-hand rule |
| Real-life examples | Fans, wheels, Earth, CDs |
| Classroom relevance | Physics Class 11 & 12 |
FAQs on Angular Velocity
What is angular velocity in simple words?
Angular velocity is the measure of how fast something rotates or spins around a point. It tells us how quickly the angle changes when an object moves in a circular path.
What is the formula for angular velocity?
The formula is:
ω = θ / t
Where:
ω is angular velocity
θ is angular displacement (in radians)
t is time (in seconds)
What is the SI unit of angular velocity?
The SI unit of angular velocity is radian per second (rad/s).
Is angular velocity a vector or scalar quantity?
Angular velocity is a vector quantity. It has both magnitude (how fast something spins) and direction (which way it spins).
What is the difference between angular speed and angular velocity?
Angular speed is a scalar quantity; it only tells how fast something is spinning.
Angular velocity is a vector quantity; it tells both how fast and in which direction the object spins.
Can angular velocity be negative?
Yes, angular velocity can be negative if the object rotates in the clockwise direction. The direction is based on the right-hand rule.
How do you calculate angular velocity from RPM?
To convert RPM (revolutions per minute) to angular velocity in rad/s:
ω = (2π × RPM) / 60
What is instantaneous angular velocity?
It is the angular velocity at a specific moment in time, like reading the speed of a rotating fan at one exact second.
What is average angular velocity?
It is calculated over a period of time:
Average ω = (Final angle - Initial angle) / (Time interval)
How is angular velocity related to linear velocity?
The formula is:
v = r × ω
Where:
v is linear velocity
r is the radius of the circular path
ω is angular velocity
What are the applications of angular velocity in real life?
You can see angular velocity in action in:
Ceiling fans
Bicycle wheels
Car tires
Washing machines
Earth’s rotation
CD/DVD players
Why is angular velocity important in physics class 11 and 12?
It helps students understand rotational motion, circular motion, and concepts like torque and moment of inertia, which are key topics in physics for Class 11 and Class 12.
What factors affect angular velocity?
Angular velocity can be affected by:
The radius of rotation
The applied force
The distribution of mass