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Updated on 10th February, 2023 , 6 min read
Momentum is a fundamental concept in physics that refers to the measure of an object's motion. It is defined as the product of an object's mass and velocity and is a vector quantity, meaning it has both magnitude and direction. The dimension of momentum is usually represented as kilogram meters per second (kg m/s), which is the standard unit of measurement for momentum in the SI (International System of Units).
Momentum is defined as the result of multiplying the mass of a particle by its velocity.
It is a vector quantity, possessing both direction and magnitude. Newton's second law states that the rate of change in momentum is equal to the force acting on a particle. This means that if a constant force is applied to a particle over a certain period of time, the product of that force and time will equal the change in momentum. Additionally, the momentum of a particle can be thought of as a measure of the time it takes for a constant force to bring the particle to rest. If either the mass or velocity of a particle is zero, its momentum will also be zero.
Mathematically, the formula is:
P = m x v
Here,
The dimension of momentum is represented as [M] and is given by the product of the dimensions of mass and velocity. In the SI (International System of Units), mass is measured in kilograms (kg) and velocity is measured in meters per second (m/s). Therefore, the dimensional formula for momentum is given as:
[momentum] = [mass] x [velocity] = kg x m/s
So, the dimension of momentum is [M] = kg x m/s. This formula shows that momentum has the dimensions of mass times velocity and is a vector quantity with both magnitude and direction. The magnitude of momentum is proportional to an object's mass and velocity, and its direction is the same as the velocity vector.
Momentum is a vector quantity that describes the motion of an object in three dimensions:
The three types of dimensions of momentum are:
These different types of momentum describe different aspects of an object's motion and are essential for understanding the physics of motion and mechanics.
The dimension of momentum can be demonstrated with an example. Let's consider a simple scenario where we have a ball with a mass of 0.1 kilograms (kg) and a velocity of 10 meters per second (m/s).
The momentum of the ball can be calculated using the equation for momentum:
p = mv = 0.1 kg x 10 m/s = 1 kg m/s
So, the momentum of the ball is 1 kilogram meter per second (kg m/s). The units for momentum are the product of the units for mass and velocity.
In this example, we can see that the dimension of momentum is the same as the product of the dimensions of mass and velocity. This formula helps us understand the physical meaning of momentum and how it is related to the mass and velocity of an object.
The momentum of a certain object is represented by the symbol ‘p'.
The mathematical equation of momentum of the object is : p = m × v
Where,
The equation above describes the fact that the mass and velocity of the particle are directly proportional to its momentum.
Hence, the SI unit that we get of the momentum of a body/ particle is the product of its mass (Kg) and its velocity (ms-1). Hence the SI unit of momentum can be written as kg ms-1.
For two particles, the momenta can be added in the following manner:
P = p1 + p2
= m1 v1 + m2 v2
In the case of more than two particles, the momentum will be added in the following way:
p = imi vi
Considering a situation in which the force is equal to the rate of change of momentum:
Force = Change in Momentum/Time Interval
Thus, Change in momentum = Force × time interval
Hence, the unit for momentum here can be written as Newton-second (Ns).
According to the CGS system, if we calculate the velocitobject/s and mass in grams, then the SI unit of momentum can be written as gram-centimeters per second i.e. (g.cm/s)
There are even a few more units of momentum, like kg×mi/hr, kg×km/hr and g×cm/s. In every case, the unit of the mass of the object is multiplied by the units of velocity.
The units of momentum are listed below:
|
Parameters |
Values |
|
SI Units |
Kilogram Meter per Second (kg.m/s) |
|
Common Symbols |
p, p |
|
Other Units |
slug.ft/s |
|
Dimension |
MLT-1 |
It is critical to take a holistic approach to every facet of a subject's chapter. It will not only adequately prepare you for the exam but will also clarify your understanding of each topic. It will help you in IIT preparation and answer conceptual problems in the exam. The number of questions from the chapter unit and dimensions would be one or two, with a weightage of roughly four marks.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readThe units of momentum will be the product of the units of mass and velocity. Mass is measured in kg and velocity in ms-1, therefore, the SI unit of momentum will be kgm/s(-1).
p = m v is the formula to calculate momentum. The equation proves that momentum is directly proportional to the object’s mass (m) and velocity (v). Therefore, the greater an object’s mass or the greater its velocity, the greater its momentum.
The SI unit of linear momentum is kg m/s.
The dimensional formula of linear momentum is [M1L1T-1].
Momentum is the quantity that is used to describe the state of motion of an object with a non-zero mass. Hence, momentum is applicable to any moving object. If is the mass of an object and is the velocity with which this body travels, then momentum can be expressed as p → = m v → .
Momentum was initially introduced by the French scientist and philosopher Descartes before Newton.
The momentum of a body is a vector quantity, for it is the product of mass, a scalar, by velocity, a vector.
Linear momentum is the product of an object’s mass and velocity in a straight line.
The origin of the use of p for momentum is unclear. It has been suggested that, since m had already been used for "mass", the p may be derived from the Latin petere ("to go") or from "progress" (a term used by Leibniz).
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