Linear momentum

In classical mechanics, linear momentum is the product of the mass and velocity of a particle, measured in $kg\cdot m{s}^{-1}=N\cdot s^{-1}$, a vector quantity:

$$\text{p}=\text{G}=m\text{v}$$

We link momentum to the sum of forces, where the integral of momentum:

$$\Sigma \text{F}=m\text{a}=m\frac{d}{dt}\text{v}=\dot{\text{G}}$$ $${\text{G}}_1+{\int }_{t_1}^{t_2}\Sigma \text{F}dt={\text{G}}_2$$

We say that the product of force and time is the linear impulse of the force.

Conservation

More useful is the idea that linear momentum is conserved, allowing us to solve a certain class of problems, i.e.,

$$\Delta \text{G}=0\to {\text{G}}_1={\text{G}}_2$$

For instance, for collision problems between two or more bodies, we can attempt to make a guess at their velocity after collision depending on what information we get, and link to conservation of energy equations:

$$m_1{v}_1+m_2{v}_2=m_{1f}{v}_{1f}+m_{2f}{v}_{2f}$$

Impulse

$$I=\Delta L=L_f-L_i=m(v_f-v_i)=F_{avg}\Delta t$$

See also

• Angular momentum