Momentum is the product of mass and velocity. Its units can be expressed as kg m/s or Ns.
Based on the definition, two objects of different masses can have the same momentum by having different velocities. For example, a pebble of 1 g traveling at 300 m/s has the same momentum as 300 g plasticine traveling at 1 m/s.
If these two objects move towards a wall, the impacts on the wall will be different.
In our daily lives, we usually avoid getting in the way of moving objects, so that we don’t get hit by them. For example, fast-moving objects (such as bullets) and slow-moving massive objects (such as a truck coming towards you at 3 m/s) will be on my list of objects.
These examples illustrate another important idea, impulse.
Impulse is the product of net force and time interval when the force is exerted. By impulse-momentum theorem, the impulse is the change in momentum. So, the product of net force and time interval equals the change in momentum.
The mathematical equation reads:
The above equation tells us one thing: for the same change in momentum, the time interval of that change affects the magnitude of the net force. In other words, the shorter the time interval, the greater the value of net force.
Back to the pebble-plasticine example, as they hit on and are stopped by the wall, they experience the same change in momentum. However, the time taken for the momentum of the pebble to change is shorter than that for the plasticine, so the net force on the pebble is greater. By Newton’s 3rd law, the force on the wall by pebble is greater than that by the plasticine. The impulsive force on the wall by the pebble is greater.
We can rearrange the above equation to get net force equals mass times acceleration.
We can also make the analogous statement: for the same change in velocity, the time interval of that change affects the magnitude of the acceleration.
The idea of momentum allows us to analyze situations such as collisions and explosions. If during that time interval the net force is zero, then there is no change in momentum – the momentum of the system (of two colliding objects or exploding pieces) does not change before and after the collision or explosion. This principle is the conservation of momentum.
This useful idea can also explain how rocket propulsion works. Neat!
Here is another example of the conservation of momentum in action.
The recoil…
Sometimes I really wonder how past people define quantities that allow us to study different situations.
Chang Physics Class 