Dimensional Formula Of Linear Momentum

Linear momentum is a concept in physics that determines the product of the mass and velocity of a particle. It evaluates the force and analyses the impact of each particle. Students must understand the concept of mass and speed before understanding linear momentum. This way, they will understand the properties of the linear momentum of a system of particles. Applying the law of conservation of momentum is also important because it helps prevent collision problems. It also analyses the system of particles moving faster. 

Dimensional Formula

The Dimensional Formula of any bodily amount is defined as the expression that represents how and which of the bottom portions are protected in that amount. It is denoted through enclosing the symbols for base portions with suitable strength in rectangular brackets, i.e., [ ].

An example is the dimension formula of Mass which is given as [M]. 

What Is Linear Momentum?

Linear momentum is the quality of a moving body that gives a certain impetus to the body. According to Newton’s second law, the rate of change of momentum of a body is called force. Thus, it is safe to say that linear momentum and its change are responsible for force.

If two particles of mass m1 and m2 are moving with initial velocity v1 and v2, respectively, both of these collide with each other, and after the collision, they stick together and move with velocity V.

From conservation of momentum:

m1v1 +m2v2 = (m1 + m2)V

So, the final velocity will be:

V = (m1v1 +m2v2 )/ (m1 + m2)

V = P/M

If the particle system is closed, then the momentum will be constant. For instance, if the particles A and B interact, the components will have an equal and opposite reaction according to Newton’s third law. If we apply the second law of Newton, then the formula becomes:

d/dt (p1+p2) = 0. 

Therefore, this example shows that the momentum of the particles (p1+p2) is constant. 

Examples Of Linear Momentum In Particles

Let us assume the mass of the particles is Z and the speed is Y. The linear momentum of the particle will then be: 

P = MV = ZxY  kg.m/s

Hence, by multiplying the values of Mass and velocity of the particles, we can get the momentum value of the particle. 

A real-life example of finding the particle’s momentum in a truck containing loads is mass B. The vehicle’s velocity is A; therefore, the momentum will be P = BxA. The truck might be supposedly tricky to stop even though the speed is slower because of the massive momentum. 

Another real-life example is a bullet. A bullet has massive momentum even with a small mass because it has an enormous velocity. 

Person A and person B are running towards each other at 6 m/sec and 7 m/sec. Since person A is running with more speed, their magnitude will also be higher. Therefore, they will quickly knock down person B, who has less magnitude due to less velocity. 

Dimensional Formula Of Linear Momentum

The dimensional formula for linear momentum is given as: 

M¹L¹T-1

Here M refers to mass, L refers to length, and T refers to time with all units in their standard form.

Derivation Of Dimensional Formula Of Linear Momentum 

The formula for momentum is given as: 

P = M × V 

Here “M” is the mass of the object, and “V” is the velocity of the same object.

Since the dimensional unit of mass is [M], and velocity is given as distance per unit of time, it means that its dimensional formula would be the ratio of length and time, i.e., [LT-1].

Combining the dimensional formulae of mass and velocity to make the dimensional formula of linear momentum, we get: 

[P] = M×LT-1

Thus, [P] = MLT-1

The dimensional formula of linear momentum is not only important for theoretical purposes but also for checking the formula of different quantities.

Conclusion

The dimensional formula of linear momentum can be calculated by applying the basic formula of the product of mass and velocity and then putting their dimensions in the formula. Linear momentum is a concept in physics that determines the product of the mass and velocity of a particle. It evaluates the force and analyses the impact of each particle. Applying the law of conservation of momentum is also important because it helps prevent collision problems. It also analyses the system of particles moving faster.