# Conservation of linear momentum

Law of conservation of linear momentum states that if there is no external force acting on two colliding objects, the momentum of the objects before the collision is equal to the momentum of the objects after the collision.

p_{1} + p_{2 }= p_{1} ’ + p_{2} ’ ………………….. Equation 1.4

m_{1 }v_{1} + m_{2} v_{2} = m_{1} v_{1 }’ + m_{2} v_{2 }’

If after collision both objects stick together,

m_{1 }v_{1} + m_{2} v_{2} = (m_{1 }+ m_{2} ) v’

where: m_{1} = mass of object 1, m_{2 }= mass of object 2, v_{1} = speed of object 1 before collision, v_{2} = speed of object 2 before collision, v_{1} ’ = speed of object 1 after collision, v_{2 }’ = speed of object 2 after collision, v’ = speed of both objects after collision

v or v’ has a positive sign if the object moves to the right and has a negative sign if the object moves to the left. If the objects’ motion directions are unknown, but both objects move in opposite directions, either of v or v’ has a positive sign while the other has a negative sign. If both objects move in the same direction, v or v’ of both objects has the same direction. The positive or negative sign indicates the direction of the object’s motion.