### 2.2 Dynamics(Linear Momentum and related concepts)

In this section we'll discuss Linear Momentum and some related concepts.

Definition: Linear momentum is the product of the mass and the velocity. Linear momentum is a vector quantity and is mostly denoted by the letter '$p$'. It's unit is $kg$ $ms^{-1}$.

Now that we have the definition of the linear momentum, we now look at the definition of the force in terms of the linear momentum. Recall that from the Newton's law of motion (in specific the $2^{nd}$ law of motion), we defined the quantity force as the product of $mass$ x $acceleration$. Here we rewrite definition of force in terms as follows,
$$F=m\frac{dv}{dt}$$
It's important to revise the definition of acceleration in order follow up. Now, if we just rewrite the above terms with the $mass$ term inside the differential we then have,
$$F=\frac{d(mv)}{dt}=dp/dt$$
where, p=mv from definition, thus we have the definition of force in terms of momentum.

Impulse: If we multiply the force acting on an object by the time it is acting for this is called the impulse of a force. Impulse is a vector and its unit is the kilogram metre per second $kg$ $ms^{-1}$ or the newton second $Ns$.

Here's a video that explains concept of an impulse with example,

Conservation of Linear Momentum:

"Conservation of momentum states that the momentum of a system is constant if there are no external forces acting on the system. It is a fundamental law of physics. So long as no external forces are acting on the objects involved, the total momentum stays the same in explosions and collisions. We say that momentum is conserved. You can use this idea to work out the mass, velocity or momentum of an object in an explosion or collision.

Here's a neat demostration of conservation of momentum,

Example Problem: A bullet with a mass of 0.02 kg leaves a gun at 1000 m/s. If the gun’s mass is 2 kg, what is the velocity of the recoil on the gun?
• momentum of bullet = mass × velocity
• = 0.02 kg × 1,000 m/s
• = 20 kg m/s
Rearrange the equation: velocity = momentum ÷ mass
• velocity of recoil on gun = 20 kg m/s ÷ 2 kg
• = 10 m/s