# Momentum Formula

## Momentum Formula

In Newtonian mechanics, Momentum Formula is the result of an object’s mass and velocity, more precisely linear momentum or translational momentum. It has both a magnitude and a direction, making it a vector quantity. If an item has mass (m) and velocity (v), then it has momentum (p). The kilogram metre per second (kg/s) is the SI unit of Momentum Formula, and it is equivalent to the newton-second. Newton’s law of motion states that all moving bodies remain in a state of motion or rest until disturbed by an outside force. The same rule applies to the Momentum Formula, meaning that if an object’s mass and speed remain constant, then its momentum will also remain constant. The Momentum Formula is the quantity of motion calculated as a product of mass and velocity, and it is related to the mass of the moving body. According to Newton’s second law of motion, the rate of change of a body’s momentum is equal to the net force acting on it. Momentum is a conserved quantity in any inertial frame, which means that if a closed system is not impacted by external forces, its total linear momentum does not change. Momentum is conserved in special relativity (with a modified Momentum Formula), as well as in electrodynamics, quantum mechanics, quantum field theory, and general relativity (in a modified version). It expresses translational symmetry, which is one of the basic symmetries of space and time. Momentum is a vector quantity, which means that it has both magnitude and direction. As the Momentum Formula has a direction, it can be used to forecast the resulting direction and speed of motion of colliding objects. The fundamental features of momentum should be learnt along with the Momentum Formula. Vector equations are nearly identical to scalar equations.

### Definition

A particle’s momentum is traditionally symbolised by the letter p. It is calculated by multiplying the particle’s mass (m) by its velocity (v). Momentum is another vector quantity. Momentum and velocity both point in the same direction. Scientists calculate Momentum Formula by multiplying the mass of the object by the velocity of the object. It indicates how difficult it would be to stop the object. The product of mass and velocity yields the unit of Momentum Formula. If the mass is in kg and the velocity is in metres per second, the Momentum Formula is in kg metres per second (kg m/s) in SI units. If the mass is in grams and the velocity is in centimetres per second in cgs units, the momentum is in grams centimetres per second (g cm/s). Momentum, being a vector, has magnitude and direction. A 1 kg model aeroplane, for example, has a momentum of 1 kg m/s due north assessed with reference to the ground when going at 1 m/s in straight and level flight. Students should learn the Momentum Formula for a thorough understanding. If someone is at the bottom of the mountain and has to choose between halting a runaway semi-truck and stopping a runaway bicycle. He will most likely choose to halt the bicycle here. This is due to the semi-truck having more momentum than the bike. The most basic definition of momentum is mass in motion. The semi-truck has greater momentum than the bike because it has more mass, but it also travels faster. Notably, the momentum is also affected by the speed. The bike has momentum because of its high speed, but since it has less mass than the truck, it has less momentum as well.

### Derivation of Conservation of Momentum

The total momentum remains constant in a closed system (one that does not interchange matter with its surroundings and is not operated on by external forces). Newton’s laws of motion imply this fact, known as the law of conservation of momentum. Consider the case of two particles interacting. The forces between them are equal in magnitude but opposite in direction, as stated by the third law. This can be established by using derivatives. This law is true regardless of how complex the force between particles is. Similarly, if there are multiple particles, the momentum exchanged between each pair of particles adds up to zero, resulting in a total change in momentum of zero. This conservation law applies to all interactions, including collisions (both elastic and inelastic) and explosive force separations. It can also be extended to situations where Newton’s laws do not apply, such as in relativity theory and electrodynamics.

### Solved Example on Momentum Formula

Solved examples on the Momentum Formula are provided by Extramarks for practice.