First Law of Motion: Qualitative aspect of force
Newton’s first law of motion states that, ” A body acted acted on by no net force has a constant velocity (which may be zero) and zero acceleration.”
From the statement we conclude that to change the state of rest or motion, an external agent is required which is called force. Hence, the first law gives the definition of force or is qualitative aspect of force.
Note: Internal force does not produce motion in total because the net internal force is zero.
Second Law of motion: Quantitative aspect of force
It states: The rate of change of momentum of a body with respect to time is directly proportional to the net external force applied on it and the change takes place in the direction of force.
We have,
$$F \propto \dfrac{dP}{dt}$$
$$F \ = \ k \dfrac{dP}{dt}$$
where k is proportionality constant. The system of units are so chosen that k=1 and $$F \ = \ \dfrac{dP}{dt}$$
$\text{or, } F \ = \ \dfrac{d}{dt}(mv)$
$\text{or, } F \ = \ m \dfrac{dv}{dt} \ + \ v \dfrac{dm}{dt}$
Normally, mass is constant so $\frac{dm}{dt} = 0$ [But in case of rocket body system mass changes. So, v*dm/dt $\neq$ 0] And, $\frac{dv}{dt}$ gives acceleration of a particle. Hence, $$F \ = \ ma$$
So, if an acceleration of 1 ms-2 is produced on a body of the mass 1 kg, then the magnitude of the force is called 1 Newton. Hence, the second law of motion describes force quantitatively.
Third Law of Motion: Effect of force
It state, “To every action there is always an equal and opposite reaction.”
If there is a force then there will always be a reaction force. Hence, gives us the effect created by force. Force always occurs in a pair because of action and reaction and isolated force doesn’t exist in nature.
Note: The action and reaction do not act on the same body but act on two different bodies. Due to this reason, action and reaction do not cancel each other. $$\text{i.e. F}_\text{a} \ = \ – \text{F}_\text{b}$$
First Law and Third Law contained in the Second law
Second law is the real law of motion other laws are just derivatives of it.
First law contained in the second law
By second law, F= ma
If F=0, a=0 which means body is either traveling with constant velocity i.e uniform motion or is at rest. This is first law.
Third law contained in the second law
If a and b be two bodies then $$\triangle \text{P} \ = \ \triangle \text{P}_\text{a} \ + \ \triangle \text{P}_\text{b}$$
Since,$$\text{F = } \displaylines{lim \\ \triangle t \rightarrow 0} \dfrac{\triangle P}{\triangle t}$$
and if $\triangle \text{P = 0}$
$$0 \ = \ F_a \times \triangle t \ + \ F_b \times \triangle t$$
$$\therefore F_a \ = \ – F_b$$
Thus, the third law is also contained in the second law.
Important Notes
- Internal force does not produce motion in total because the net internal force is zero.
- The first law gives qualitative definition of force.
- The second law gives quantitative definiton of force.
- The third law explains the effect of application of force.
- The action and reaction do not act on the same body but act on two different bodies. Due to this reason, action and reaction do not cancel each other.
- Newton’s first law and third law are contained in the second law.
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