Impulse and Momentum Calculator
Free calculate impulse, momentum change, force, and time using the impulse-momentum theorem. solve for any variable.
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What are Impulse and Momentum?
Impulse is the product of force and the time over which it acts (J = F×t). Momentum is the product of mass and velocity (p = mv). The impulse-momentum theorem states that impulse equals the change in momentum: J = Δp.
This relationship explains why increasing collision time reduces impact force (airbags, crumple zones), and why momentum is conserved in collisions. Impulse is measured in N·s (Newton-seconds), the same units as momentum (kg·m/s).
Understanding impulse and momentum is crucial in sports, automotive safety, engineering, and any situation involving collisions or force applications over time.
Impulse and Momentum Formulas
Impulse
Force × time
Momentum
Mass × velocity
Impulse-Momentum Theorem
Impulse equals change in momentum
How to Calculate
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1
Identify what to solve for
Determine whether you need impulse, force, time, or momentum change.
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2
Convert to SI units
Convert all values to Newtons, seconds, kilograms, and meters per second.
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3
Apply the appropriate formula
Use J = F×t for impulse, F = J/t for force, t = J/F for time, or J = m(v_f - v_i) for momentum change.
Practical Examples
Example 1: Constant Force
A 100 N force acts on an object for 0.5 seconds. Calculate the impulse.
Solution:
J = F × t = 100 N × 0.5 s
J = 50 N·s
Example 2: Momentum Change
A 2 kg object changes velocity from 0 m/s to 10 m/s. What impulse was applied?
Solution:
J = m × (v_f - v_i) = 2 kg × (10 - 0) m/s
J = 20 N·s
Example 3: Airbag Safety
A person's momentum changes by 1000 N·s during a crash. If an airbag extends the collision time to 0.1 s, what is the average force?
Solution:
F = J / t = 1000 N·s / 0.1 s
F = 10,000 N (much less than without airbag!)
Applications
Automotive Safety
Airbags, crumple zones, and seatbelts increase collision time to reduce impact force and protect passengers.
Sports
Understanding how follow-through increases impulse, and how padding reduces impact forces in contact sports.
Engineering
Designing shock absorbers, impact protection systems, and understanding collision dynamics.
Rocketry
Calculating thrust impulse, momentum transfer, and understanding rocket propulsion principles.
Frequently Asked Questions
Why do airbags reduce injury?
Airbags increase collision time, reducing impact force for the same momentum change. Since F = J/t, longer time means lower force.
What is the difference between impulse and momentum?
Momentum (p = mv) is a property of moving objects. Impulse (J = F×t) is the change in momentum caused by a force acting over time.
Is momentum conserved in collisions?
Yes, in isolated systems (no external forces), total momentum is conserved. This is the law of conservation of momentum.
Why is follow-through important in sports?
Follow-through increases the time force is applied, increasing impulse and thus the change in momentum of the ball or object.
Can impulse be negative?
Yes, if force opposes motion, impulse is negative, indicating a decrease in momentum. The direction matters in vector calculations.