Impulse & Momentum Calculator

General Physics

Calculate impulse, momentum, force, or velocity based on the impulse-momentum theorem. Select the variable you want to find.

Practical Examples

Load an example to see how the calculator works.

Baseball Bat Hit

Find Final Velocity

A baseball (0.145 kg) is pitched at 40 m/s. A bat applies a force of 6500 N for 0.0015 s. What is the ball's final velocity?

Calculation Type: findFinalVelocity

Mass: 0.145 kg

Initial Velocity: 40 m/s

Force: 6500 N

Time: 0.0015 s

Car Collision

Find Average Force

A 1500 kg car traveling at 15 m/s collides with a wall and stops in 0.15 s. What was the average force exerted on the car?

Calculation Type: findForce

Mass: 1500 kg

Initial Velocity: 15 m/s

Final Velocity: 0 m/s

Time: 0.15 s

Rocket Engine Burn

Find Time Duration

A 500 kg rocket accelerates from 100 m/s to 150 m/s. If its engine produces a constant thrust of 25000 N, how long did the engine burn for?

Calculation Type: findTime

Mass: 500 kg

Initial Velocity: 100 m/s

Final Velocity: 150 m/s

Force: 25000 N

Bouncing Ball

Find Impulse

A 0.5 kg basketball hits the floor at -8 m/s and bounces back up at 6 m/s. What is the impulse delivered by the floor to the ball?

Calculation Type: findImpulse

Mass: 0.5 kg

Initial Velocity: -8 m/s

Final Velocity: 6 m/s

Other Titles
Understanding the Impulse and Momentum Calculator: A Comprehensive Guide
Dive deep into the physics of impulse, momentum, and their relationship as described by Newton's Second Law. This guide will walk you through the concepts, formulas, and practical applications.

What is Impulse and Momentum?

  • Defining Momentum
  • Defining Impulse
  • The Impulse-Momentum Theorem
Momentum and impulse are two fundamental concepts in classical mechanics, crucial for analyzing objects in motion, especially during collisions or when forces act over short time intervals.
Defining Momentum (p)
Momentum is often described as 'mass in motion.' It is a vector quantity, meaning it has both magnitude and direction. An object's momentum is the product of its mass (m) and its velocity (v). The formula is:
p = m * v
A massive truck moving slowly can have the same momentum as a light baseball moving very fast. Understanding momentum is key to analyzing how objects interact.
Defining Impulse (J)
Impulse is the change in momentum of an object. It's not just about the force applied, but also how long that force is applied. Impulse is calculated as the product of the average force (F) and the time interval (Δt) over which it acts. The formula is:
J = F * Δt
This shows that a small force applied for a long time can produce the same change in momentum as a large force applied for a short time.
The Impulse-Momentum Theorem
This theorem is the cornerstone of our calculator. It directly links impulse and momentum by stating that the impulse applied to an object is equal to the change in its momentum (Δp). Mathematically, it combines the two previous formulas:
J = Δp = pfinal - pinitial = mv_final - mv_initial
Therefore, we get the powerful equation: F Δt = m (vfinal - vinitial). Our calculator uses different arrangements of this formula to solve for the unknown variable.

Step-by-Step Guide to Using the Impulse and Momentum Calculator

  • Selecting the Calculation Type
  • Entering Input Values
  • Interpreting the Results
Our calculator is designed to be flexible, allowing you to solve for different variables in the impulse-momentum equation. Here's how to use it effectively.
1. Selecting the Calculation Type
Start by using the 'Calculation Type' dropdown menu to choose what you want to find. You can solve for: Final Velocity, Average Force, Time Duration, or simply Impulse (from a change in velocity).
2. Entering Input Values
Based on your selection, the necessary input fields will appear. For example, to find the 'Final Velocity', you will need to provide the 'Mass', 'Initial Velocity', 'Average Force', and 'Time Duration'. Fill in all the required fields with your known values. Ensure you are using the correct units as specified (kg, m/s, N, s).
3. Interpreting the Results
After clicking 'Calculate', the results will be displayed. The calculator will show the impulse (or momentum change) along with the primary variable you were solving for. The units for impulse are Newton-seconds (N·s), which are equivalent to kilogram-meters/second (kg·m/s).

Real-World Applications of Impulse and Momentum

  • Vehicle Safety Systems
  • Sports Science
  • Rocket Propulsion
The principles of impulse and momentum are not just academic; they are applied everywhere in engineering and daily life.
Vehicle Safety Systems
Airbags and crumple zones in cars are prime examples of impulse manipulation. In a collision, the car's momentum must change to zero. To reduce the force on the occupants, safety features increase the time (Δt) over which this change occurs. By increasing Δt, the average force (F) is significantly decreased, making the collision more survivable.
Sports Science
In sports like baseball, golf, or tennis, athletes aim to maximize the impulse they deliver to the ball. They achieve this by applying a large force and maintaining contact for as long as possible (the 'follow-through'). This maximizes the change in the ball's momentum, resulting in higher velocity and greater distance.
Rocket Propulsion
Rockets work based on the principle of conservation of momentum. They expel high-velocity exhaust gas (mass) in one direction. To conserve momentum, the rocket gains an equal amount of momentum in the opposite direction, causing it to accelerate. The impulse is the thrust (force) provided by the engine over the time it burns.