Linear momentum

Linear momentum is a vector quantity defined as the product of an object’s mass  m and its velocity v. Linear momentum is denoted by the letter p .

Note that a body’s momentum is always in the same direction as its velocity vector. The units of momentum are kg m/s.

p=mv

Law of conservation of linear momentum 

The total linear momentum of a system of interacting bodies on which no external forces are acting        remains constant.

Collisions

Let a constant force (f) act in the same direction in which the particle is moving . Initial and final velocities are u and v,time taken – t.                                                                                                                           Ft is an important quantity in dynamics.It has been named as impulse.

A large force(F)  acting in a very small time interval(t)                                                                                          Then      Impulse I = F×t

Impulse is a vector quantity.Direction of impulse is the direction of force.

I=Ft=Δ(mv)                     Unit –  kgms^-1

Applications

(i) A cricket player lowers has hands while catching the ball : by doing so the time of impact increases and hence the effect of force decreases.

(ii) When a person falls from a certain height on floor, he receives more injuries as compared to falling on a heap of sand. It is because the Cemented floor does not yield whereas the sand yield there by increasing the time of impact hence decreasing the impact of force.

(iii) The shock absorbers provided in the vehicle helps to travel smoothly on an uneven road. It is because the shockers increases the time of impulse which reduces the force.

 In a force – time graph area between the graph and the time axis gives the impulse.

Area=F×t=impulse

Force due to water flow

Conveyor belt

Force on helicopter blades