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His first law of motion states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.

That means, delta(a) = 0 if external F = 0. ..... (i)

His second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

That means, delta(a) = F/m. ...... (ii)

If we put F = 0 in eq. (ii), then we get delta(a) = 0. But wait! Isn't this exactly what first law says? So is first of law a corollary of the second law? And if so, why the obviously-not-stupid Newton proposed it as another law rather than proposing a corollary? Are we missing something?

Qmechanic
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Himanshu Mishra
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1 Answers1

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Yes the first and second law are indeed similar. However you fail to take into account of the period of which he proposed the laws. During that time, it was obvious that if one were to roll a ball on a smooth surface, the ball would eventually stop although no forces were seemingly acting on it.

The first law states that an object will continue moving in a straight line or remain stationary unless a force acts on it. So to explain this, Newton gave the second law and called the opposing force friction. Then it was obvious to everyone that the ball would stop rolling even though it looked like no forces were acting on it.

So while it is obvious to us, it may not be so for the people at that time and thus required to laws to explain.

Horus
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