Momentum Calculator — Step-by-Step Solutions

The Momentum Calculator helps you solve momentum problems step by step. Calculate linear momentum (p = mv), impulse (J = F times t), and analyse two-body collisions including both elastic and inelastic types.

Enter your values and get instant results with detailed working. The calculator covers four modes: linear momentum, impulse and change in momentum, conservation of momentum for two-body collisions, and elastic versus inelastic collision analysis.

Mass (kg)

Velocity (m/s)

Your calculations will appear here

How to Use the Momentum Calculator

Select a calculation mode: Linear Momentum, Impulse, Conservation, or Collision.
For Linear Momentum, enter the mass (kg) and velocity (m/s). The calculator computes p = mv.
For Impulse, enter the force (N) and time interval (s). The calculator computes J = F times delta t.
For Conservation, enter the masses and velocities of two objects. The calculator finds the final velocity after a perfectly inelastic collision.
For Collision, choose elastic or inelastic, then enter masses and velocities. The calculator shows final velocities and kinetic energy changes.

Formula and Theory

Momentum is the product of an object's mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of momentum is kg m/s.

The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum: J = delta p = F times delta t. This connects force acting over time to changes in motion.

The law of conservation of momentum states that in an isolated system (no external forces), the total momentum before and after a collision remains the same. This principle applies to all types of collisions.

In an elastic collision, both momentum and kinetic energy are conserved. In a perfectly inelastic collision, momentum is conserved but the objects stick together and kinetic energy is lost (converted to heat, sound, or deformation).

Worked Examples

Example 1: Linear momentum

Problem: A 5 kg ball moves at 3 m/s. What is its momentum?

Solution: p = mv = 5 times 3 = 15.

Answer: 15 kg m/s

Example 2: Impulse

Problem: A force of 200 N acts on a ball for 0.05 s. What is the impulse?

Solution: J = F times delta t = 200 times 0.05 = 10.

Answer: 10 N s

Example 3: Perfectly inelastic collision

Problem: A 4 kg cart at 6 m/s hits a stationary 2 kg cart. They stick together. Find the final velocity.

Solution: m1*v1 + m2*v2 = (m1+m2)*vf. So 4*6 + 2*0 = 6*vf. vf = 24/6 = 4.

Answer: 4 m/s

Example 4: Elastic collision

Problem: A 2 kg ball at 5 m/s hits a 3 kg ball at rest. Find the final velocities (elastic).

Solution: v1f = ((2-3)/(2+3))*5 = -1. v2f = (2*2/(2+3))*5 = 4.

Answer: v1f = -1 m/s, v2f = 4 m/s

Frequently Asked Questions

What is the difference between momentum and kinetic energy?

Momentum (p = mv) is a vector and is always conserved in collisions. Kinetic energy (KE = 0.5mv squared) is a scalar and is only conserved in elastic collisions.

Can momentum be negative?

Yes. Momentum is a vector, so its sign indicates direction. A negative momentum simply means motion in the opposite direction to the chosen positive axis.

What is the difference between elastic and inelastic collisions?

In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not. In perfectly inelastic collisions, the objects stick together.

Why does impulse equal change in momentum?

From Newton's second law, F = ma = m(delta v / delta t). Rearranging gives F times delta t = m times delta v = delta p. The product of force and time equals the change in momentum.

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