← Momentum and impulse

The unit of momentum

A 2.0 kg cart rolls at 3.0 m/s. Its momentum is 6.0. Six what? A bare number is not a measurement.

Momentum needs a unit of its own. Which unit?

Momentum is mass times velocity: p = mv.

Mass carries kilograms. Velocity carries meters per second.

The cart's recordquantityvaluemass2.0 kgvelocity3.0 m/smomentum6.0 ?
The momentum's number is missing its unit.

Multiply the quantities, and the units multiply too: kilograms times meters per second.

The SI unit of momentum is the kilogram-meter per second, written kg·m/s.

The raised dot marks the multiplication: kilogram times meter, all per second.

Quantity, unit, symbolquantitySI unitsymbolmasskilogramkgvelocitymeter per secondm/smomentumkilogram-meter per secondkg·m/s
Multiply the quantities, and the units multiply too.

So the cart's momentum is written p = 6.0 kg·m/s, and a momentum of 12 kg·m/s is twice as much.

Which is the SI unit of momentum?

A 5.0 kg dog runs at 4.0 m/s. Its momentum is 20 ___. Which unit completes the value?

Every momentum value carries this unit.

A lab report states a cart's momentum as 15 kg·m/s. Is the unit correct for a momentum?

The SI unit of momentum is the kilogram-meter per second, written kg·m/s.

A 4.0 kg cart moves at 2.0 m/s, so p = 4.0 × 2.0 = 8.0. Write the momentum with its unit.

Mass in kilograms times velocity in meters per second gives kg·m/s.

p = 8.0 kg·m/s.

A record reads: momentum = 9.5 kg. What is wrong with the record?

kg is the unit of mass alone.

A momentum is mass times velocity, so its unit multiplies kg by m/s.

The record should read 9.5 kg·m/s.

Your turn

A lab record reads: mass 2.5 kg, velocity 2.0 m/s, momentum 5.0 ___. Which unit completes the record?

Which measurement could be a momentum?

A student writes a cart's momentum as 6.5 m/s. What is wrong with the record?