Introduction

The mass of a body refers to the total amount of matter present within it. All matter is made up of atoms and molecules. Thus, when we say that an object has a mass of "n kg", what we mean is that the sum of the masses of its atoms and molecules is "n kg". Further, we are aware that the motion of a body can be described in terms of its velocity and acceleration. However, velocity alone isn’t sufficient to determine the effect of motion and instead, we use a quantity known as the momentum for the same. In this article, we will try to understand what mass and momentum mean.

What is Mass?

The total amount of matter present within a body is known as its mass and mathematically, we can calculate it as

m denotes the mass of the body.

ρ denotes the density of the body.

V denotes the volume of the body.

From experience, you would know that trying to push an empty box is far easier than trying to push a box filled with heavy objects like bricks. Scientifically, this is related to the concept of mass, and objects with a larger mass require more force for moving. Thus, we can say that the mass of an object also measures its ability to resist a change in its state of motion. This property is known as inertia and has enormous applications in physics. 

You should remember that mass is a scalar quantity and thus, does not depend on direction. In SI units, it is measured in kilograms (kg)

What is Weight?

The weight of an object is related to the amount of force it exerts on the ground due to Earth’s gravitational pull. Since the gravitational pull of all planets is different, the weight of objects also differs from planet to planet. Mathematically, the weight of an object on Earth is:

W=mg

Here m denotes the mass of the body and g denotes the acceleration due to the gravity of Earth, equal to 9.8 m/s². The concept of weight is different from that of mass, though the former depends on the latter. Here are a few important distinctions between the two.

What is Momentum

As previously stated, velocity alone isn’t enough to fully appreciate the effect of the motion of a body. Instead, we use a quantity known as momentum, which is defined as the product of an object’s mass with its velocity. That is,

Naturally, since velocity is a vector quantity, momentum is also a vector and its direction are along the direction of the velocity of the object. The following graph describes how the momentum of an object can be resolved along the three coordinate axes if an object is moving in three dimensions.

Linear Momentum in three dimensions.

Law of Conservation of Linear Momentum

The law of conservation of linear momentum is a universal rule which is stated as follows: “If the net external force acting on a system is zero, its linear momentum remains conserved”. That is, regardless of the events occurring inside the system, if there is no external force on the system, the total linear momentum of its components will remain constant. This law is related to Newton’s second law of motion and is derived using Newton’s third law. Here is an example of this law in action:

Consider two cars A and B of masses m and M moving towards each other with velocities u and U, respectively. Assume that we are only talking about a one-dimensional case. If the two cars collide, their velocities will change. Let us call their new velocities as v and V. In such a case, the law of conservation of momentum states that if there is no external force on this system of cars, then the total linear momentum before and after the collision remains unchanged. That is,

Notice that the law is stated in vector terms, which means that linear momentum is conserved along all three directions.

Variation of Momentum with the Mass of the body

We have already stated the formula for linear momentum . This means that momentum is directly proportional to the mass of an object. From this observation, we can understand the physical significance of momentum using the following examples:

1. A car of mass 100 kg is moving towards a wall with a speed of 50 m/s. It comes to a halt after hitting the wall.

2. A large truck, of mass 1000 kg is moving with the same velocity and it also comes to a halt after hitting the wall.

From common observation, you will be able to say that out of the above cases, the truck is sure to cause far more damage to the wall than the car since it is heavier. This is the concept of momentum. Mathematically:

Hence, since the momentum of the truck is ten times that of the car, the effect of its motion and strike on the wall is 10 times as great as the car. This way, the physical significance of momentum can be understood.

Summary

Mass is related to the amount of matter present inside an object, whereas weight is the force exerted by an object due to the gravitational pull of the planet. Momentum is related to both the mass and velocity of an object and measures the effect of motion by considering both these quantities. It is defined as the product of mass and velocity and remains constant when the net external force on the system is zero.

Frequently Asked Questions

Q1. Does the mass of the moving body always remain constant?  

Under most practical scenarios, the mass of an object does not change. However, at speeds that are comparable to the speed of light (), the mass of an object starts to increase.

Q2. Give a real-life example of the conservation of Momentum.

When a soldier shoots a gun, he feels its recoil on his body. This is because the gun imparts a large amount of momentum to the bullet, which is counterbalanced by the recoil of the gun by the law of conservation of momentum.

Q3. What does the rate of change of momentum tell us?

The time rate of change of momentum equals the force on an object, as defined by Newton’s second law of motion. This can also be proven as follows:

Therefore,

Q4. What is the relation between angular and linear momentum?

Angular momentum is the rotational analog of linear momentum and mathematically, it is given as the cross-product of linear momentum with the distance from the axis of rotation. It is also known as the moment of momentum.

Q5. What do you mean by the center of mass?

The center of mass of an object is that point at which we can assume its entire mass to be concentrated. The study of the center of mass can help us simplify several problems in physics.