How this instrument works
Momentum is what a moving object carries by virtue of moving: mass multiplied by velocity, p = m·v. The formula says mass and speed trade off exactly — a 1,500 kg car creeping along at 2 m/s and a 250 kg motorcycle-plus-rider at 12 m/s carry the same 3,000 kg·m/s. That trade-off is the whole idea, and it is why a slow, heavy thing can be as hard to stop as a fast, light one.
Physics keeps strict books on this quantity. In any collision — billiard balls, cars, subatomic particles — the total before equals the total after, provided no outside force intervenes. That is why crash investigators reconstruct impact speeds from wreckage masses, and why a rifle recoils: the bullet's forward share must be balanced by the gun's backward share. Force, in Newton's own formulation, is simply the rate at which momentum changes.
The unit, the kilogram-metre per second, has no shorter name, though it is identical to the newton-second — the unit of impulse. Push on something with one newton for one second and you have added exactly one kg·m/s. This sheet handles magnitudes: enter mass and speed and it returns the size of the momentum; direction is yours to keep track of.
- Enter the mass in the Mass field — kilograms by default, with grams, tonnes, and pounds on the unit menu.
- Enter the speed in the Speed field; km/h and mph are converted to metres per second before multiplying.
- Read the Momentum (kg·m/s) line — the product m·v to one decimal place, with the substitution shown in the working block.
Worked example — a family car at highway speed
A 1,500 kg car travelling at 27.78 m/s — what the speedometer reads as 100 km/h. Momentum: p = 1,500 × 27.78 = 41,670 kg·m/s, which the instrument reports to one decimal place as 41,670.0.
That figure is what the brakes must remove to stop the car. Spread the stop over 10 seconds of gentle braking and the average force is 41,670 ⁄ 10 = 4,167 newtons; hit a wall and the same change happens in a tenth of a second, demanding a hundred times the force. Same p, very different afternoon.
Questions
Is momentum the same as kinetic energy?
No. Momentum is m·v, linear in speed; kinetic energy is ½·m·v², quadratic. Double a car's speed and its momentum doubles while its energy quadruples. Collisions always conserve momentum; they only conserve kinetic energy when perfectly elastic, which real crashes never are. The two answer different questions — momentum governs recoil and impulse, energy governs damage and heating.
Can momentum be negative?
In full vector form, yes — it points along the velocity, so motion in the negative direction of your chosen axis carries a negative value, which is how opposing momenta cancel in collisions. This instrument works with speed, the magnitude of velocity, and so returns a magnitude; assign the sign or direction yourself when balancing a two-body problem.
What is the unit of momentum?
The kilogram-metre per second (kg·m/s), which is exactly the same unit as the newton-second (N·s) used for impulse — a reminder that force applied over time is precisely what changes momentum. There is no specially named SI unit for it; reference tables simply write kg·m/s.
Why does the calculator convert my units before multiplying?
Because p = m·v only holds when the units agree. The instrument converts every input to SI base form — pounds become kilograms (1 lb = 0.45359237 kg exactly), mph and km/h become metres per second — multiplies, and reports kg·m/s. Type 3,300 lb and 62 mph and the arithmetic actually runs on 1,496.9 kg and 27.7 m/s.
What is impulse, and how does it relate to momentum?
Impulse is force multiplied by the time it acts, and it equals the change in momentum it produces — the impulse–momentum theorem, a restatement of Newton's second law. Airbags and crumple zones exploit it: they cannot reduce the amount a crash must remove, but by stretching the stop over more time they cut the peak force your body feels.