Linear momentum of a system of particles

Introduction

The linear momentum (P) of an object is the product of its mass (M) and velocity (V). The formula is, therefore, P=MV. The property of linear momentum not changing is known as Conservation of Momentum, which is especially applicable in cases where the external force of the particles is zero, then the linear momentum of the system of particles remains constant. This law is essential to remember for it aids in the calculation of an object’s linear momentum. Momentum is also known as the quantity of motion. This article focuses on the properties, definitions, and examples of momentum.

Linear Momentum of System of Particles

Listed below are some features of linear momentum and the process of calculating the linear momentum:

1. The formula of linear momentum is P=MV, as mentioned above.
2. Newton understood the importance of the component and highlighted the law of motion in terms of the same in his second law of motion.
3. The second law of Newton describes the importance of momentum. It states that moment is applicable in any object considering the changing mass systems. However, the relationship between force and mass is more functional when the object’s mass is a constant factor.
4. The second law of Newton considers various factors- the relationship of the change in mass and the force and the direction of the force.
5. The formula of Newton’s second law for a single particle is F= dP/dt, where  F denotes the force of the concerned particle. If the number of particles in the momentum is n, the formula becomes :                                                                                                                    P = P₁ + P₂ +….+P_n .

The momentum is written as P = m₁ v₁ + m₂ v₂ + ….+m_nv_n   P = ∑m_nv_n P = MV

1. The center of the object’s mass lies on the plane of symmetry.
2.  The center of the object’s mass does not necessarily need to lie within the same thing. It may be located anywhere inside or outside the particle.

Since momentum includes direction, it determines the direction and speed of the object while they are in motion and after they collide. It is present in both elastic and inelastic collisions of the entities. If the crash occurs with friction or significant air resistance, the bodies moving to the air must be considered.

Impulse and Linear Momentum of System of Particles

Changing momentum is also related to the period of the force. A slight momentum change occurs if the force is applied in short periods. But if the force is more significant, then the particle’s momentum is more remarkable. Therefore, the quantity of impulse becomes force x time interval. For instance, if the force is F and the dt is the time duration of the force, then the F=dP/dt, according to the second law of Newton. Furthermore, the dp becomes dp= F dt. Greater force and lesser force are interrelated to each other. The impact a more significant force can create in a short period is equivalent to that of a small force that is applied for an extended period.

Examples of Linear Momentum of System of Particles

Listed below are some examples of linear momentum in particles: 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 collision they stick together and move with velocity V. From conservation of momentum m₁v₁ +m₂v₂ = (m₁ + m₂)V So 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. Another example of linear momentum is: 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 kgm/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 is a truck containing logs 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.

Conclusion

Therefore, linear momentum is a concept in physics that determines the product of the mass and velocity of a particle. It evaluates the force of each particle 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.