# Angular Motion: Definition of Angular Motion, Relationship between Linear and Angular Motion (For CBSE, ICSE, IAS, NET, NRA 2022)

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In Physics, just as there are formulas to calculate linear velocity and displacement, there are also equivalent formulas to calculate angular movement.

## Definition of Angular Motion

• Angular motion is defined as, the motion of a body about a fixed point or fixed axis. It is equal to the angle passed over at the point or axis by a line drawn to the body.
• Objects don՚t always travel in straight lines. For situations involving circular motion, such as the pendulum of a clock, or a door swinging, it՚s often easier to solve problems by looking at the angular motion of the objects.

## Relationship between Linear and Angular Motion

• Displacement – In linear motion, we use ′ x to quantify the linear distance travelled. In angular motion, we use ′ θ for the same to quantify the angular distance, and it is measured in radians.
• Velocity – In linear motion, we use v to denote velocity while in angular motion, we use ′ ω to indicate angular velocity. Angular velocity is the number of radians covered per second.
• Acceleration – We use ′ a to denote linear acceleration, while we use ′ α to mean the angular acceleration. The unit for angular acceleration is radians per second square.
• Momentum: In linear motion, we use p to denote momentum while in angular motion, we use ′ L to indicate angular velocity.
• Kinetic energy: In linear motion, we use ′ K ′ to denote momentum while in angular motion, we use ′ K to indicate angular velocity.
• Force: In linear motion, we use F to denote momentum while in angular motion, we use ′ to indicate angular velocity.
• Newton՚s second law of motion: In linear motion, we use F to denote momentum while in angular motion, we use ′ to indicate angular velocity.
• Mass: In linear motion, we use ′ M ′ to denote momentum while in angular motion, we use ′ I ′ to indicate angular velocity

### Table Shows a Relationship between Linear and Angular Motion

 Linear motion term In symbols Angular motion term In symbols Magnitude of angular terms (if v, a and F are perpendicular to r the radius) Displacement Angular displacement Velocity Angular velocity ​​ Acceleration Angular acceleration ​ Momentu​​m Angular momentum Kinetic energy Kinetic energy Force F​ Torque (or moment) Newton՚s Second Law of motion Angular version of Newton II Mass M Moment of inertia
• One can work out angular equations of motion, like those for linear motion, provided the angular acceleration alpha, α is constant
• For an object rotating about an axis, every point on the object has the same angular velocity.

### What is an Angular Velocity?

The tangential velocity of any point is proportional to its distance from the axis of rotation. Angular velocity has the units rad/s.

• Angular velocity , is the rate of change in angular displacement (radians per second) .

• Angular velocity can also be given as the frequency of revolution, f (rev/s or rpm) :

### Equation of Angular Versus Linear Velocity

 Angular Linear
• where is the angular speed at time t = 0
• Δθ is the angular displacement.