# 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 | | ||

Momentum | 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) :

### Angular Velocity

### Equation of Angular Versus Linear Velocity

Angular | Linear |

- where is the angular speed at time t = 0
- Δ
*θ*is the angular displacement.