Momentum Calculator

General Physics

Calculate the momentum and kinetic energy of an object. Enter the mass and velocity below.

Practical Examples

Use these examples to see how the calculator works in real-world scenarios.

Moving Car

Car

Calculate the momentum of a standard car moving on the highway.

Mass: 1500 kg, Velocity: 25 m/s

Fired Bullet

Bullet

Determine the momentum of a small bullet right after being fired.

Mass: 0.01 kg, Velocity: 700 m/s

Sprinting Athlete

Runner

Find the momentum of an athlete during a sprint.

Mass: 70 kg, Velocity: 5 m/s

Rolling Bowling Ball

Bowling Ball

Calculate the momentum of a bowling ball as it rolls down the lane.

Mass: 7 kg, Velocity: 8 m/s

Other Titles
Understanding Momentum: A Comprehensive Guide
Explore the fundamental concepts of momentum, its calculation, applications, and the physics behind it.

What is Momentum?

  • Defining Momentum in Physics
  • The Core Formula: p = mv
  • Units of Momentum
In physics, momentum is a fundamental concept that describes an object's quantity of motion. It is often referred to as 'mass in motion.' All objects have mass, so if an object is moving, it has momentum. It is a vector quantity, meaning it has both magnitude and direction. The direction of the momentum is the same as the direction of the object's velocity.
The Core Formula
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). The formula is simple and powerful:
p = m * v
This equation shows that momentum is directly proportional to both the mass and the velocity of an object. If you double the mass or the velocity, you double the momentum.
Units of Measurement
In the International System of Units (SI), the unit for momentum is kilogram-meters per second (kg·m/s). This is derived directly from the units of mass (kg) and velocity (m/s).

Simple Momentum Calculation

  • An object with a mass of 10 kg moving at 5 m/s has a momentum of 10 kg * 5 m/s = 50 kg·m/s.
  • A 2000 kg truck at rest (velocity = 0 m/s) has zero momentum.

Step-by-Step Guide to Using the Momentum Calculator

  • Inputting Mass and Velocity
  • Interpreting the Results
  • Resetting for a New Calculation
Our Momentum Calculator is designed for ease of use. Follow these simple steps to get your results instantly.
Step 1: Enter Mass
In the 'Mass (m)' field, type the mass of your object. Ensure that the mass is in kilograms (kg) for an accurate SI unit calculation.
Step 2: Enter Velocity
In the 'Velocity (v)' field, enter the object's velocity. This value should be in meters per second (m/s).
Step 3: Calculate
Click the 'Calculate' button. The calculator will instantly display the object's momentum and its kinetic energy.
Interpreting the Results
The results section will show 'Momentum (p)' in kg·m/s and 'Kinetic Energy (KE)' in Joules (J). Kinetic energy is included because it's closely related to momentum, representing the energy of motion.

Using the Calculator

  • To find the momentum of a 70 kg person running at 3 m/s, enter 70 for mass and 3 for velocity.
  • For a 0.5 kg ball thrown at 20 m/s, enter 0.5 and 20 into the respective fields.

Real-World Applications of Momentum

  • Vehicle Safety and Collisions
  • Rocket Propulsion Systems
  • Sports Science
Momentum isn't just a textbook concept; it's a critical principle that governs many real-world phenomena.
Vehicle Safety Engineering
In car crashes, the concept of momentum is paramount. Engineers design safety features like airbags and crumple zones to increase the time over which the car's (and passenger's) momentum changes, which reduces the force of impact (Impulse-Momentum Theorem).
Rocket Propulsion
Rockets work based on the principle of conservation of momentum. A rocket expels hot gas (mass) at high velocity in one direction, causing the rocket to gain an equal and opposite amount of momentum in the other direction, propelling it forward.
Sports Science
In sports like billiards, bowling, or baseball, understanding momentum is key to predicting the outcomes of collisions. A batter must impart maximum momentum to the ball, and a billiards player uses momentum transfer to sink shots.

Application Examples

  • A cricket player pulls their hands back while catching a ball to increase the time of impact, reducing the force on their hands.
  • In billiards, a cue ball stops dead after hitting another ball head-on, transferring all its momentum to the target ball.

Common Misconceptions and Correct Methods

  • Momentum vs. Kinetic Energy
  • The Law of Conservation of Momentum
  • Is Momentum Always Conserved?
Understanding the nuances of momentum helps avoid common errors in physics.
Distinguishing Momentum and Kinetic Energy
While both relate to motion, they are different. Momentum (p = mv) is a vector, while Kinetic Energy (KE = 0.5 m v^2) is a scalar. An object can have momentum but no kinetic energy is impossible if it's moving. Two objects with opposite velocities but the same mass and speed will have a total momentum of zero, but a significant total kinetic energy.
Conservation of Momentum
One of the most fundamental laws in physics is the law of conservation of momentum. It states that for an isolated system (one with no external forces), the total momentum remains constant. This is why the total momentum before a collision equals the total momentum after the collision.
When is Momentum Not Conserved?
Momentum is not conserved if there are external forces acting on the system. For example, the momentum of a single falling ball is not conserved because the external force of gravity is acting on it. However, if you consider the system of (ball + Earth), their combined momentum is conserved.

Conceptual Clarifications

  • If two identical cars traveling at the same speed collide head-on, their total initial momentum is zero. After they crumple together and stop, their total final momentum is also zero, conserving momentum.
  • A rocket in deep space conserves momentum, but a car braking to a stop does not, as friction from the road and brakes are external forces.

Mathematical Derivation and Examples

  • Deriving Momentum from Newton's Second Law
  • Calculating Kinetic Energy
  • Worked-Out Numerical Examples
The formula for momentum is deeply connected to Newton's laws of motion.
Connection to Newton's Second Law
Newton's Second Law is often stated as F = ma, but its more general form is F = dp/dt, where F is the net external force and dp/dt is the rate of change of momentum. If mass is constant, F = d(mv)/dt = m(dv/dt) = ma, which gives the more common form of the equation. This shows that force is the rate at which momentum changes.
Kinetic Energy Calculation
The kinetic energy (KE) represents the work needed to accelerate an object from rest to its stated velocity. The formula is:
KE = 1/2 m v^2
Our calculator provides this value alongside momentum for a more complete analysis of the object's motion.

Worked-Out Examples

  • Example 1: A 1000 kg car moving at 20 m/s. Momentum p = 1000 kg * 20 m/s = 20,000 kg·m/s. Kinetic Energy KE = 0.5 * 1000 kg * (20 m/s)^2 = 200,000 Joules.
  • Example 2: A 0.15 kg baseball thrown at 40 m/s. Momentum p = 0.15 kg * 40 m/s = 6 kg·m/s. Kinetic Energy KE = 0.5 * 0.15 kg * (40 m/s)^2 = 120 Joules.