# How to calculate change in momentum

**Introduction**

Momentum is a fundamental concept in physics, and understanding how to calculate changes in momentum can help you better grasp the behavior of moving objects. In this article, we will explore the meaning of momentum, how it works in various scenarios, and a step-by-step guide on how to calculate changes in momentum.

**What is Momentum?**

Momentum (denoted as p) is defined as the product of an object’s mass (m) and its velocity (v). The equation for momentum is:

**p = m * v**

Momentum is a vector quantity, which means it has both magnitude and direction. It also has units of mass (usually kilograms) multiplied by velocity (measured in meters per second).

**Change in Momentum**

The change in momentum is the difference between an object’s initial and final momentum. This change can occur due to various forces acting on the object, such as gravity, friction, or an applied force.

To calculate the change in momentum (Δp), you subtract the initial momentum (p_initial) from the final momentum (p_final). The equation for change in momentum is:

**Δp = p_final – p_initial**

Calculating Change in Momentum: A Step-by-Step Guide

Here’s a step-by-step guide on how to calculate changes in an object’s momentum:

**Step 1: Identify initial and final velocities**

Determine the initial and final velocities of the object. These can be given or obtained through experimentation or observation.

**Step 2: Determine mass**

Find out the object’s mass. In most cases, this information will be provided.

**Step 3: Calculate initial and final momenta**

Using the equation for momentum (p = m * v), calculate both the initial and final momenta by multiplying each velocity by the object’s mass.

**Step 4: Find the change in momentum**

Use the change in momentum equation (Δp = p_final – p_initial) to subtract the initial momentum from the final momentum. The result will indicate the change in momentum.

Example Problem

Let’s consider an example for clarity:

A 2 kg ball is moving at an initial velocity of 5 m/s. After colliding with a wall, it rebounds and has a final velocity of -3 m/s. Calculate the change in momentum.

Solution:

**Step 1: Identify initial and final velocities**

Initial velocity (v_initial) = 5 m/s

Final velocity (v_final) = -3 m/s

**Step 2: Determine mass**

Mass (m) = 2 kg

Step 3: Calculate initial and final momenta

Initial momentum (p_initial) = m * v_initial = 2 kg * 5 m/s = 10 kg*m/s

Final momentum (p_final) = m * v_final= 2 kg * (-3 m/s) = -6 kg*m/s

Step 4: Find the change in momentum

Δp = p_final – p_initial = (-6 kg*m/s) – (10 kg*m/s) = -16 kg*m/s

So, the change in momentum is -16 kg*m/s.

**Conclusion**

Understanding how to calculate changes in momentum helps improve our grasp of physics concepts and real-world applications. By following these simple steps, you can quickly and accurately calculate changes in momentum for any situation.