Linear momentum is the quantity of motion of a moving body due to its mass and velocity. But what does this mean? How does it make sense that motion is a quantity? Well, if you've ever played football, you'll know that when you stop the ball with your foot, it pushes against your foot. This is because the ball has momentum and it transfers that momentum into your foot. However, you can also imagine a bowling ball and a golf ball moving towards you at the same speed. It would be much harder to stop the bowling ball then the golf ball because the bowling ball has a greater mass, and therefore a greater momentum.
The linear momentum of an object can be found by multiplying the mass of said object by is velocity:
p = mv
p = linear momentum
m = mass of the object
v = velocity of the object
Linear momentum is measured in kgms⁻¹ or Ns (newton seconds).
Example: What is the momentum of a dog running if it has a mass of 60 kg and is moving at a constant velocity of 30 km/h?
First, you convert the 30 km/h to m/s:
30 km/h × 1000/3600 = 8.3 m/s
Then we put these values into the formula for momentum:
p = mv
= 60 kg × 8.3 m/s
= 498 kgms⁻¹
If you remember Newton's Laws of motion, you will know that his second law can be summarized like this:
F = ma
We can write this in terms of linear momentum:
F = m(v-u)/t
F = mv - mu/t (mv would be final momentum and mu would be initial momentum)
F = Δp/t
This shows that the net external force acting on an object is equal to the change in momentum over time. (Remember that Δ (delta) means the change in)
We can use this to answer certain questions that involve forces:
Example: A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. Compute the time required for a force of 1500 N to bring the car to rest.
The first thing we can do here is to find the momentum:
p = mv
= 15000 kg × 5.4 m/s
= 81000 kgms⁻¹
Now that we know the momentum, we can use newton's second law written in terms of momentum to find t, time:
F = p/t
1500 N = 81000 kgms⁻¹/t
t = 81000 kgms⁻¹/1500 N
t = 81000 Ns/1500 N (remember that kgms⁻¹ can also be written as Ns)
t = 54 s