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Question
Suppose we define a quantity 'Linear momentum' as linear momentum = mass × speed.
The linear momentum of a system of particles is the sum of linear momenta of the individual particles. Can we state principle of conservation of linear momentum as "linear momentum of a system remains constant if no external force acts on it"?
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Solution
The question assumes the existence of linear momentum, which is the product of a particle's mass and speed.
The linear momentum of a system of particles is equal to the total of the linear momentum of each of the system's constituent particles. The question of whether a principle that states that the system's linear momentum stays constant in the absence of an external force is then posed.
First, we examine a straightforward system of two particles to validate the claimed principle.
Assume the two particles possess identical velocities while moving in opposing directions along the x-axis. Designate the velocities of each particle as v, with each possessing an identical mass, m.
Assume the external force is zero.
The linear momentum of the system is mv + mv = 2 mv
Because these particles are travelling in opposite directions, they will clash. Assume the collision is perfectly inelastic. Then, using the conservation of linear momentum, we can conclude that both particles will come to rest following the collision.
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