Hello dear students we have learnt that, the tendency of body to resist change of its state of motion is termed as inertia of motion. External force is required to change the state of from motion to rest.
When object is in motion, along with mass, velocity also contributes inertia. Here the product of mass and velocity i.e. momentum provides the inertia. So stop the moving object we have to change momentum of the object. To stop running car, we need to apply brakes so that the momentum of car is opposed by brakes and car slows down. Running fan doesn’t stops immediately after switching it off, its due to the momentum of fan cannot be completely resist by frictional force caused by air, so that fan continues to rotates , until and unless its momentums becomes zero. The relation between force and momentum can be explained with the help of Newton’s second law of motion.
Let’s learn the Newton’s second law of motion in detail……!
When there is change in momentum of body, force associated with it also changes.
Statement: Rate of change of momentum is directly proportional to the impressed force, and the change in momentum is takes towards the direction of applied force.
Consider the object of mass ‘m’ changes its velocity from v to v + ∆v in time dt. Hence the change in momentum can be given as,
(Since the mass of object is constant)
Let’s illustrate the law in simple form…………!
Suppose the bullet of mass ‘m’ is thrown on wall with velocity of v1, so that the initial momentum of bullet can be,
P1= mv1.
Now imagine that after time ‘t’ the same bullet is fired with help of gun on the same wall with velocity of v2, then its momentum will be,
P2= mv2.
Now we can easily predict that the impact on wall in 2nd case will be higher than that of 1st case, then change in momentum can be
∴∆P = P2 – P1
∴∆P = mv2 – mv1
∴∆P = m (v2 – v1) ………………….(1)
According to second law of motion, we can have,
F α rate of change of momentum
As the mathematical form for force was given by Newton, hence the SI unit of force is named after him, i.e. netwon (N)
Equation (2) and (3) are the mathematical forms of Newton’s second law of motion.
Importance of Newton’s Second Law of Motion:
- It gives mathematical formula for measurement of force as rate of change of linear momentum.
- It gives momentum as the fundamental quantity related to motion not only velocity.