Education

# What is Angular Momentum and Linear Momentum?

## What is momentum?

Like velocity and acceleration, momentum is the basic term in physics, of any moving body. It is defined as the quantity of motion of an object. Any object that is in motion, has momentum. It is also defined as mass in motion. Everything has some mass, so as any object starts moving, it gains momentum. An object with more mass and velocity will have large momentum. Usually momentum is mixed with its sub term: linear momentum that is actually a type of momentum. Momentum is a vector quantity as it is related to moving objects & definitely all moving objects has some velocity, which is a vector. Its unit is Kg.m/s. There are a lot examples of momentum to understand it. Linear and angular momentum are two types of momentum.

• A semi-truck filled of logs, definitely has a large mass and it must slow down a long before a stop light. Because even when its velocity will be very small, it will have a large momentum and is difficult to stop.
• A bullet that seems to have very small mass, possesses a large momentum due to extremely large velocity. ## Types of momentum

Momentum is of two types

• Linear momentum
• Angular momentum

### What is linear momentum?

The product of mass of body and its velocity is known as linear momentum. When an object is moving in a line, or executing linear motion then it has linear momentum. Linear momentum formula is given by

p = m v

Here velocity v is a vector and p indicates linear momentum, thus linear momentum is also a vector quantity. The SI unit of momentum is Kg.m/s.

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### Linear momentum and Newton’s second law

According to Newton’s second law of motion, if force F is applied on an object then acceleration is produced in it, that is given by

F = ma

Since a = Δv / Δt

So F = m Δv / Δt

F = ΔP / Δt

It is the relation between force and momentum which can be stated as “force acting on a body is equal to rate of change of momentum”. This is applicable either mass is constant or varying (like in case of rocket).

### Impulse and momentum

From the derived relation, momentum can also be linked to the impulse. Since impulse is the product of force and time so

F x Δt = ΔP

Hence impulse is equal to the change in momentum.

### What is angular momentum?

When an object is moving in a circle then it has angular momentum. It is the property of an object that characterizes the rotational inertia of that object. Angular momentum is defined as the cross product of linear momentum and the perpendicular distance r. It is also a vector quantity and is indicated by L. Angular momentum formula is given by

L = m v r

Since p = m v

So L = p r

Where r is the perpendicular distance between the axis of rotation and the object of mass m. in angular momentum since body moves in circle so it is also linked to the angle and is basically given as

L = m ( v x r )

Both v and r are vectors. L is perpendicular to the plane made by v and r.

L = m v r Sinθ

Or L = r x p

“Angular momentum is the cross product of the perpendicular distance and the linear momentum.” The direction of angular momentum can be found by the right hand rule as shown: For a rigid body, angular momentum is defined as the product of moment of inertia (I) and angular velocity (ω).

L = I ω

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## What is law of conservation of momentum?

Law of conservation of momentum states that “the total momentum of a system remains constant i.e. the total momentum before collision and after collision remains same. For example, explosion of bomb, firing a bullet from rifle, collision of 2 objects and rocket motion etc. let’s understand it in detail.

In case of bomb explosion, let the actual mass of bomb is “M” and V is initial velocity, as it explodes it is divided into fragments of different masses (let m1, m2 etc) having different velocities v1, v2 etc. Now the sum of momentum of each of this fragment is exactly equal to the actual momentum of bomb. This is the law of conservation of momentum. MV = m1v2 +m2v2 + …….

During this explosion energy is wasted in form of sound, heat and to break bomb into fragments etc. so energy also remains conserved during this explosion, as law of conservation of energy states that “energy cannot be created or destroyed however it can change form from one to another”.