Mass and Momentum - Definition, Example, FAQs

What is Mass?

Mass is a fundamental property of matter that specifies the amount of matter contained in an object. It has magnitude but no direction, hence it is a scalar quantity.

According to Newton's second law of motion:

$$
F=m a
$$

where $m$ is the mass.

Unit of Mass

SI Unit of mass: Kilogram (kg)
Other units include grams ( g ), metric tons ( t ), and in atomic physics, atomic mass units (amu).

Difference Between Mass and Weight

Mass: A measure of the amount of matter in an object (in kg ) is Mass.
Weight: The force due to gravity acting on the mass is called as a Weight.

$W=\mathrm{m} \mathrm{g}$

where

• $W$ is weight,
• $m$ is mass, and
• $g$ is the gravitational acceleration.

How are inertia and mass related?

Objects with more mass have more inertia than an object with a smaller mass.

This means that inertia is directly proportional to the mass. We need to apply more unbalanced force to move an object with more mass than an object with light mass.

For example – we can easily move a chair from its initial position than to move a sofa.

Mass and Velocity

The relationship between mass ( $m$ ) and velocity ( $\mathbf{v}$ ) is called linear momentum ( $\mathbf{p}$ ):

$$
\mathbf{p}=m \mathbf{v}
$$

• Mass is scalar, and velocity is vector, so momentum (p) is a vector quantity with the same direction as velocity.
• The SI unit of momentum is $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$.
• Momentum measures the difficulty of stopping an object and is crucial in analyzing collisions and motion.

Also read -

• NCERT Notes For All Subjects
• NCERT Solutions for All Subjects
• NCERT Exemplar Solutions for All Subjects

What is momentum?

Momentum is defined as the product of the mass and velocity of that object. Momentum is a measure of the time required through constant force to put an object at rest. Being a vector quantity it gives both the direction and magnitude.

The SI unit of momentum is kilogram meter per second ( $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ ).

Momentum Formula

$$
\mathbf{p}=m \mathbf{v}
$$

where:

• $\mathbf{p}$ is the momentum (a vector quantity),
• $m$ is the mass of the object (scalar),
• $\mathbf{v}$ is the velocity of the object (vector).

Conservation of Momentum

Law of Conservation of Linear Momentum is a fundamental concept in Physics stating that the total momentum of an isolated system remains constant, provided no external forces act on the system. This law applies to all physical systems, including particles, objects, and even large-scale systems like galaxies.

Mathematical Statement of Conservation of Momentum:

$\mathbf{p}_{\text {initial }}=\mathbf{p}_{\text {final }}$

Proof of Momentum Conservation

From Newton's second law:

$$
\mathbf{F}=\frac{d \mathbf{p}}{d t}
$$
If the net external force $\mathbf{F}_{\text {net }}$ on the system is zero:

$$
\frac{d \mathbf{p}}{d t}=0
$$
This implies that $\mathbf{p}$, the momentum, is constant over time.

Applications of Conservation of Momentum

The concept of Conservation of Momentum is applied to :

• Elastic Collision: Both momentum and kinetic energy are conserved.
• Inelastic Collision: Momentum is conserved, but kinetic energy is not (some energy is converted to other forms like heat or deformation).
• Rocket Propulsion: Rockets work based on momentum conservation. As exhaust gases are expelled backward, the rocket gains forward momentum.