Impulse and Momentum Calculator
Calculate impulse, momentum, and analyze motion dynamics with physics formulas
Calculate Impulse and Momentum
Mass of the object
Velocity before impulse
Velocity after impulse
Physics Results
Key Formulas:
• Momentum: p = m × v
• Impulse: J = m × Δv = m × (v₂ - v₁)
• Impulse-Momentum Theorem: J = Δp
Physics Analysis
Example: Ball Stopping
Problem Setup
Scenario: A 160g ball moving at 2.5 m/s is caught and stopped
Mass: m = 160 g = 0.16 kg
Initial velocity: v₁ = 2.5 m/s
Final velocity: v₂ = 0 m/s (stopped)
Solution
1. Calculate velocity change: Δv = v₂ - v₁ = 0 - 2.5 = -2.5 m/s
2. Apply impulse formula: J = m × Δv
3. J = 0.16 kg × (-2.5 m/s) = -0.4 N⋅s
Result: Impulse = -0.4 N⋅s (negative indicates deceleration)
Real-World Examples
Car Collision
Car stopping from 72 km/h
Baseball Pitch
Baseball being pitched
Bullet Impact
Bullet stopped by target
Tennis Ball Serve
Tennis ball serve
Key Physics Concepts
Momentum
Quantity of motion (p = mv)
Impulse
Change in momentum (J = Δp)
Force
Applied push or pull (F = J/t)
Change
Delta symbol for differences
Impulse-Momentum Theorem
The Theorem
J = Δp = F⋅Δt
Impulse equals change in momentum
Units
N⋅s = kg⋅m/s
Newton-seconds
Applications
- • Vehicle collisions
- • Sports impacts
- • Rocket propulsion
- • Safety design
Understanding Impulse and Momentum
What is Momentum?
Momentum is a fundamental concept in physics that describes the quantity of motion of an object. It's calculated as the product of an object's mass and velocity (p = mv). Momentum is a vector quantity, meaning it has both magnitude and direction.
What is Impulse?
Impulse is the change in momentum of an object. It can be calculated in three ways: from the change in momentum (J = Δp), from mass and velocity change (J = mΔv), or from force and time (J = Ft). The impulse-momentum theorem states that these are all equivalent.
Key Formulas
Momentum
p = m × v
Mass times velocity
Impulse (Method 1)
J = Δp = p₂ - p₁
Change in momentum
Impulse (Method 2)
J = m × Δv
Mass times velocity change
Impulse (Method 3)
J = F × t
Force times time
Real-World Applications
Vehicle Safety
Airbags increase collision time, reducing force
Sports
Tennis racket hitting ball, boxing gloves
Rocket Propulsion
Exhaust gases create impulse for thrust
Industrial
Hammer impacts, pile driving
Important Principles
Conservation of Momentum
Total momentum remains constant in isolated systems
Vector Nature
Direction matters - momentum is a vector quantity
Sign Convention
Positive/negative indicates direction of change
Time Dependence
Longer impact time reduces peak force