Unit of Momentum -SI Unit, CGS Unit & Other Units, FAQs

Edited By Vishal kumar | Updated on Sep 24, 2024 06:15 PM IST

In this article students will learn about the Newton’s third law of motion, momentum, SI units of the momentum, Linear momentum , SI Unit of the Linear momentum, CGS unit of the momentum, rate of change of momentum, unit of rate of change of momentum,

What is Momentum?

Momentum is an outcome of Newton's third law of motion. When two objects collide, the colliding objects exert equal and opposite forces on each other. Each of these objects can sense unequal forces acting on them, but the entire system has no force acting at all. According to Newton's law of motion, the total impulse experienced by an object depends on the force acting on it. The momentum remains unchanged in the absence of external forces. An important idea in Newtonian mechanics is that when two objects collide, the overall momentum remains unchanged before and after the collision. An impulse can be mathematically defined as the product of an object's mass and its velocity. The sum of the mass multiplied by the velocity before and after the impact should be the same.

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What is Momentum?
Define momentum and its SI Unit
Conservation of Linear Momentum Principle

Unit of Momentum -SI Unit, CGS Unit & Other Units, FAQs

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Mathematically, it’s a product of mass and velocity of the objects. In the physics community it is denoted by the letter p

Hence p=m*v

………1

Where m – Mass of the object

v- Velocity of the object

Units of the Momentum

SI unit of the momentum (Unit of linear momentum is)	kg•m/s.
CGS Unit of the momentum	g⋅cm/s
SI unit of rate of change of momentum	Newton (N)
Unit of angular momentum	kg-m2/sec

Define momentum and its SI Unit

Momentum can be defined as "moving mass". All items have mass; so if an object moves, it has momentum, and its mass is in motion. The amount of momentum an object has depends on two variables: the amount of material it moves and the speed of the material's movement. The momentum depends on the mass and speed variables. In terms of the mathematical equation, the momentum of a body is nothing but the product of the mass of the object times its velocity.

Momentum = Mass • Speed

………2

In physics, the lowercase p is the symbol for momentum. Thus, the equation for the momentum can be rewritten as

p = m • v

………3

In above equation it can be seen that, the momentum of the object is directly proportional to the mass of the object m and velocity of the object v. Equation 3 is also called as the linear momentum and its SI unit is Kg. m/s

So if the velocity of the object is increases keeping mass constant the momentum of object are also increases same is true for vice versa.

Momentum units are units of mass multiplied by units of velocity. The SI unit of momentum is kg • m / s. Although kg • m / s is the standard metric unit of momentum, there are many other units that are accepted (though not traditional) units of momentum. Examples include kg · mph, kg · km / h, and g · cm / s. In each of these examples, the unit of mass is multiplied by the unit of speed to obtain the unit of momentum. This is in line with the momentum equation.

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For the two mass systems total momentum of the system can be written as

P = m1v1+ m2v2

………4

Now consider the system whose mass is constant, then differentiating above equation with respect to time will give

dpdt=m1dV1dt+m2dV2dt

………5

In above equation dv1dt is rate of change of velocity called as the acceleration unit being m/s2

dpdt=m1a1+m2a2

………6

But we know that from Newton’s 2nd Law of motion rate of change of momentum is equal to the force. Hence above equation can be expressed in terms of force as

F=m1a1+m2a2

………7

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Conservation of Linear Momentum Principle

From our last equation 7, we now consider the special case when F = 0. This means that no external forces act on the isolated particle system. This situation implies that the rate of change of the total momentum of the system does not change, which means that this value is constant and confirms the principle of conservation of linear momentum: When there is no net external force acting on the particle system, the total momentum of the system is preserved. It's that simple. Regardless of the nature of the interactions occurring in a given system, its overall momentum will remain the same. To see exactly how this concept works, let's look at an example.

Keep the linear pulse in action. Consider cannon that fire a cannonball. Initially, both the cannon and the cannonball are stationary. Since the gun, bullet and explosive are in the same particle system, we can conclude that the total momentum of the system is zero. What happens after cannon is fired? It is clear that the cannonball is thrown with considerable speed and therefore with momentum. Since the system is not acted on by purely external forces, this impulse must be compensated for by an impulse in the direction opposite to the speed of the ball. In this way, the gun itself gains reverse speed while maintaining overall momentum. This conceptual example explains the "strike" associated with a firearm. Each time a gun, cannon, or artillery element fires a projectile, it must move in the opposite direction of the projectile. The heavier the firearm, the slower it moves. This is a simple example of conservation of momentum.

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Frequently Asked Questions (FAQs)

1. Define and explain Newton's third law of motion?

According to Newton's third law, forces act in pairs, and the forces are equal and opposite. For example, when two objects collide, the colliding objects exert equal and opposite forces on each other.

2. What is centripetal and centrifugal acceleration?

A sphere orbiting someone's head demonstrates the forces of centripetal and centrifugal acceleration. The force applied to hold the ball in place is called centripetal acceleration. At the same time, the force that the ball perceives from them is called centrifugal acceleration.

3. What is an example of the law of conservation of angular momentum?

The law of conservation of angular momentum says that when an object is not affected by any external force, the angular momentum does not change. An example of this is a spinning top where it will spin unless friction slows it down.

4. What is the relationship between the momentum of a body and the force acting on it?

According to the Newton’s law, Force is a rate of change of momentum over time. It can be written as F = mass x acceleration. In practical terms, the momentum of an any body increases when a force is acting upon it increases, because the force is responsible for it to accelerate, and to have an increase in its velocity.

5. What is angular momentum? Explain with an example.

In physics there are systems which are rotational in motion for example planetary motion. The angular momentum is equivalent to the linear momentum in term of rotations. It is also a conserved quantity. The angular momentum of any system which is closed is always remain constant. It is denoted by the letter L and mathematically can be expressed as

L = mvr

Example of the angular momentum conservation is planetary motion.