# Momentum

# Momentum

**This lesson aligns with Next Generation Science Standards (NGSS) PS2.B**

**Introduction**

To understand the nature of the matter, it is essential to know some basic concepts such as inertia, mass, momentum, velocity, speed, distance, etc. Momentum is a commonly used term that is associated with the mass in motion. The object that is moving has momentum which can be measured by the mass and the velocity of the moving object. The law of conservation of momentum is a fundamental law that is used to describe the momentum of a system of objects. In this article, we will learn about momentum, the dependence on momentum, and the law of conservation of momentum.

**Momentum**

Momentum is a vector quantity that is used to explain the motion of an object with non-zero mass. The term non-zero mass defines that it is only applicable to any moving object. For instance, a ball with some mass is moving at a particular speed possesses momentum.

**Factors affecting Momentum**

The momentum of a moving object depends upon both the mass and the velocity of that object. The momentum of a moving object can be calculated by using the following formula.

*Momentum = mass × velocity*

As we know, mass is measured in kilograms, and velocity is measured in meters per second, so the unit of momentum is kilogram-meters per second or kgm/s. Momentum is described by the magnitude of velocity as well as the direction of the moving object. Mass is a scalar quantity, so the momentum of the object is in the same direction as its velocity.

If two objects move in the same direction then the momentum will depend on their masses. The massive an object is, the more momentum it has. For example, a car has more momentum than a football because it has greater mass.

Similarly, the greater the velocity of an object, the more momentum it has. For instance, a baseball moving at 30 m/s will have more momentum than a baseball moving at 8 m/s. In addition, it is harder to change the velocity of the baseball that is moving at 30 m/s than the velocity of the baseball moving at 8 m/s.

**Conservation of Momentum**

The word conservation has a more specific meaning that refers to the condition before and after some event. When two moving objects exert force on each other for a short time or bump into each other, this is known as a collision.

The law of conservation of momentum states that the total momentum of the two objects before the collision is the same as the total momentum after the collision. In other words, the total momentum of any group of objects remains constant during an interaction, provided that no external force is acting on the system. Friction is a common example of external force.

**Collision with Two Moving Objects**

Newton’s third law is applied, when two moving objects collide with each other. During a collision, both objects experience force that is equal in magnitude and opposite in direction. This type of force causes one object to speed up and another object to slow down.

For example, two balls have equal masses moving on the same path as shown in the figure. The red ball is moving down at 6 m/s whereas the blue ball is moving at 3 m/s. The red ball reaches the blue ball and collides with it. Due to collision, the velocity of each ball changes. The red ball slows down to 3 m/s while the blue ball speeds up to 6 m/s. Hence, the total momentum is conserved.

collision between two balls will change the speed of each

**Collision with One moving Object**

If the red ball is traveling at 6 m/s and the blue ball is at rest. Eventually, the red ball collides with a blue ball. After the collision, the red ball will stop moving but the blue ball moves at 6 m/s. Although the situation is different now, the total momentum is conserved that has been transferred from one ball to another.

**Collision with Connected Objects**

Imagine two balls are soft and collide with each other. When they collide, instead of bouncing off each other, they stick together. After the collision, the coupled balls have twice the mass and the velocity of the coupled balls will be 3 m/s half of the initial velocity of the red ball. Hence total momentum is conserved as the mass is doubled and the velocity becomes half.

**Summary**

- Momentum refers to a quantity that is used to explain the state of the motion of objects with non-zero mass.
- Momentum depends on the mass and the velocity of the moving object, and It can be expressed as p= mv.

The law of conservation of momentum states that total momentum may be transferred from one body to another but not destroyed at all.

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