Momentum Calculator
Our mechanics calculator computes momentum accurately. Enter measurements for results with formulas and error analysis.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Momentum Calculator
Calculator
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Formula: p = m × v
Worked example — Final velocity = 2 m/s (momentum conserved: 12 kg*m/s before and after)
Formula
p = m × v
Momentum equals mass times velocity.
Worked Examples
Example 1: Collision of Two Carts
Problem:A 4 kg cart moving at 3 m/s collides with a stationary 2 kg cart and they stick together (perfectly inelastic collision). What is the final velocity?
Solution:Initial momentum = m1*v1 + m2*v2 = (4)(3) + (2)(0) = 12 kg*m/s After sticking together, combined mass = 6 kg Final velocity = total momentum / combined mass = 12 / 6 = 2 m/s
Result:Final velocity = 2 m/s (momentum conserved: 12 kg*m/s before and after)
Example 2: Rifle Recoil
Problem:A 4 kg rifle fires a 0.01 kg bullet at 400 m/s. What is the rifle's recoil velocity?
Solution:Bullet momentum = 0.01 kg x 400 m/s = 4 kg*m/s (forward) By conservation of momentum, rifle momentum must be -4 kg*m/s Recoil velocity = -4 / 4 = -1 m/s
Result:Recoil velocity = 1 m/s backward
Frequently Asked Questions
What is momentum and why does it matter?
Momentum (p) is the product of an object's mass and velocity, p = mv, measured in kg·m/s. It matters because in a closed system with no external forces, total momentum is always conserved — this single rule lets you solve collision and recoil problems without ever knowing the details of the forces involved during impact.
How do you calculate momentum for a moving object?
Multiply mass in kilograms by velocity in meters per second. A 10 kg object moving at 5 m/s has momentum p = 10 × 5 = 50 kg·m/s. Because velocity is a vector, momentum also has direction — two objects with equal mass and speed but opposite directions have equal and opposite momentum.
How is momentum different from kinetic energy?
Momentum (p = mv) scales linearly with velocity, while kinetic energy (KE = ½mv²) scales with velocity squared. Doubling an object's speed doubles its momentum but quadruples its kinetic energy. This is why a car crash at twice the speed is far more than twice as destructive — the energy that must be dissipated rises much faster than the momentum.
What is conservation of momentum used for?
Conservation of momentum lets you find unknown velocities after a collision or explosion without needing to know the forces involved. In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision (like a car crash where vehicles crumple together) momentum is still conserved but kinetic energy is lost as heat and deformation.
How does momentum explain recoil in a gun or rocket?
Before firing, total momentum is zero. When a bullet is fired forward with momentum p_bullet, the gun must recoil backward with equal and opposite momentum p_gun = -p_bullet so the total stays zero. Because the gun's mass is much larger than the bullet's, its recoil velocity is proportionally much smaller — the same principle that propels rockets forward by ejecting exhaust mass backward.
What is impulse and how does it relate to momentum?
Impulse equals the change in momentum, J = Δp = FΔt, where F is the average force and Δt is the time over which it acts. This is why airbags and crumple zones reduce injury: stretching the stopping time (Δt) for the same change in momentum reduces the average force experienced by occupants.
What is momentum and how is it conserved?
Momentum is p = mv (mass times velocity). In a closed system with no external forces, total momentum is conserved. In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not. Impulse (F*t) equals the change in momentum.
References
Background & Theory
Momentum in Everyday Collisions
Linear momentum p = mv is one of the most reliable tools in mechanics because, unlike force, it's conserved in any closed system regardless of how complicated the internal collision forces are. This makes it possible to solve for post-collision speeds without ever measuring the actual (often very brief and hard-to-measure) forces involved in an impact.
| Object | Typical mass | Typical speed | Approx. momentum |
|---|---|---|---|
| Thrown baseball | 0.145 kg | 40 m/s (fastball) | ~5.8 kg*m/s |
| Rifle bullet (.308) | 0.0098 kg | 850 m/s | ~8.3 kg*m/s |
| Sedan car | 1,500 kg | 27.8 m/s (100 km/h) | ~41,700 kg*m/s |
| Loaded cargo ship | 50,000,000 kg | 7 m/s (~13.6 knots) | ~350,000,000 kg*m/s |
The huge momentum figure for a cargo ship explains why large vessels take miles to stop even at modest speed — bringing that momentum to zero requires either a very large force or a very long time (impulse J = FΔt = Δp), and neither is available in an emergency stop at sea.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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