Momentum calculator: p = mv with working

Example: a 1,200 kg car travels at 15 m/s. $p = 1200 \times 15 = 18000$ kg m/s.

In a closed system (no external forces), the total momentum before a collision or explosion equals the total momentum after it.

Example: a 2 kg trolley moving at 3 m/s hits a stationary 1 kg trolley and they stick together. Momentum before $= 2 \times 3 + 1 \times 0 = 6$ kg m/s. After, the combined mass is 3 kg, so $v = 6 \div 3 = 2$ m/s. You can check that last step with the calculator: momentum 6, mass 3.

In an explosion (like a gun firing), the total momentum before is zero, so afterwards the two parts move in opposite directions with equal and opposite momentum.

Force equals the rate of change of momentum: $F = \dfrac{m\Delta v}{\Delta t}$. Spreading a change in momentum over a longer time means a smaller force. That's why crumple zones, airbags, seat belts and cycle helmets work: they increase the time the collision takes, so the force on the person is smaller.

Momentum is in kg m/s (sometimes written kg·m/s). Masses in grams need converting to kilograms and speeds in km/h need dividing by 3.6 before multiplying; the calculator shows both steps if you choose those units.

Example: a 160 g cricket ball bowled at 108 km/h. Mass = 0.16 kg and speed $= 108 \div 3.6 = 30$ m/s, so $p = 0.16 \times 30 = 4.8$ kg m/s.

• Ignoring direction: in a head-on collision, one velocity must be negative.
• Adding speeds instead of momenta.
• Forgetting a stationary object has zero momentum (but still counts in the mass afterwards if they stick).

Practise with our momentum questions and see how momentum links to F = ma.

• Draw a quick before-and-after sketch with arrows and label each mass and velocity.
• Write "momentum before = momentum after" as a line of working: it earns credit even if the arithmetic slips.
• In explosions and recoil questions, the total momentum before is usually zero.
• State the unit, kg m/s, and the direction if the question asks for velocity.