Linear momentum, sometimes simply call as momentum is the product of mass of the object and its velocity in the given direction. Linear momentum is a vector quantity and its direction will be same as the velocity of the object.
It can be formulated as-
G ⃗ = mV ⃗
Fig. 7.1 shows the linear momentum of an object about a point O
Differentiation the above equation, we get-
(dG ⃗)/dx = m (dV ⃗)/dx
= m a ⃗
(dG ⃗)/dx = ∑▒□(F ⃗ )
Or,
∑▒□(F ⃗ ) = G ̇ ⃗
Where,
∑▒□(F ⃗ )= Resultant of forces. It can be calculated as-
Resultant Force,
∑▒□(F ⃗ )= ∑▒Fxi ̂ +∑▒Fyj ̂+ ∑▒Fzk ̂
= G ̇xi ̂ +G ̇yj ̂+ G ̇zk ̂
Or,
∑▒Fx = G ̇x
∑▒Fy= G ̇y
∑▒Fz= G ̇z
Note:
The S.I. unit of Linear Momentum is kg. m/s
