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In physics, linear momentum is a vector quantity that is defined as the product of mass and velocity. In simple words, the product of a mass of an object m and its velocity v determines the linear momentum of the object. The alphabet ‘p’ is used to signify momentum in short and combines both m and v. Moreover, the momentum of a body is always in the same direction in which it has a velocity vector. Being a conserved quantity it denotes that the total momentum of a system is constant. The unit of linear momentum is expressed as kg m/s.

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The linear momentum formula is expressed as :

p= m*v

We can express the dimensional formula of linear momentum as follows:

[m1 l1 t^{-}1]

Where,

M = mass

L = length

T = time

Derivation

Linear Momentum Formula = mass × velocity. . . . . . (i)

Linear momentum dimensional formula,

Mass = [m1 l0 t0] . . . . (ii)

Velocity = [m0 l1 t-1] . . . . (ii)

By substituting equation (ii) and (iii) in equation (i) we can obtain,

Linear Momentum = mass × velocity

or, L = [m1 l0 t0] × [m0 l1 t-1] = [m1 l1 t-1].

Hence, the dimensional representation of linear momentum is [m1 l1 t-1].

By applying newton’s second law of motion we can explain the conservation of the linear momentum formula. The rate of change of linear momentum formula of a body is equal to the net force applied to the body.

Mathematically it is expressed as:

dP/dt

= mv/dt

= m dv/dt

= ma

= Fnet

The importance of linear momentum of a body or a system is that it retains the total momentum. This is equal to the product of vector velocity and mass is given that there is no external force acting on it.

FAQ (Frequently Asked Questions)

1. What is the Conservation of Linear Momentum?

The law of conservation of linear momentum explains if the net external force applied to a body is zero, then the momentum of an object remains constant. It has to be noted that the momentum of the object is conserved and not of every particle. The momentum of each body in the object will increase or decrease depending upon the situation. However, the momentum of the system will always be conserved as long as there are no external forces acting or applied to it. The conservation of linear momentum gives us an idea that the linear momentum of isolated systems remains constant.

2. Explain the Conservation of Momentum Formula?

The conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force applied on the colliding objects.

Mathematically, the conservation of momentum formula expresses that the momentum of the system remains constant when net external force remains zero.

This means that, initial momentum= final momentum

Pi= Pf

Law of conservation of momentum formula

This is mathematically expressed in terms of the given formula

p=m *v

where,

p is the linear momentum

m is the mass of the body

v is the linear velocity

3. State the Applications of Conservation of Linear Momentum?

The biggest example of an application of conservation of linear momentum is in the launching of the rocket. When the rocket fuels are burned, it pushes the exhaust gases downwards and due to this, the rocket gets further pushed upwards. On a similar principle, the motorboat also functions. It pushes the water backwards and gets pushed forward in a reaction to conserve momentum. Let’s explain this with an example. Suppose, a bomb is at rest before the explosion. At this time the momentum is zero. When it explodes, it breaks open into several parts, each part having its own momentum. A piece will move in one direction with a certain speed and another piece will move in the opposite direction with the same momentum.