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Question

State Newton's second law of motion and show that the first law of motion can be mathematically stated from the Newton's seconds law.


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Solution

Newton's first law of motion:

  • It states that “Every object continues to be in the state of rest or uniform motion in same direction unless a net external force is acted upon it.”

Newton's second law of motion:

  • It states that “The rate of change of momentum of a body is directly proportional to the force applied, and takes place in the same direction in which the force acts.”
  • According to this law, ForceRateofchangeinmomentum.

Deriving first law of motion from second law of motion:

  • According to son law, Momentum is the product mass and velocity, p=mv.
  • So, the rate of change of momentum can be written as p=mv-mu, where v is the final velocity and u is the initial velocity.
  • Then, rate of change of momentum will be

Rateofchangeofmomentum=pt=mv-mut=mv-ut

  • This can be further written as Rateofchangeofmomentum=ma, since v-ut=a, where a is the acceleration.
  • Thus it is obtained that, “Net force applied on a body is equal to rate of change of momentum”, F=pt, since force is the product of mass and acceleration, F=ma.
  • This implies, if net force is zero, the body will continue to move with same velocity.
  • This leads to the first law of motion, according to which until external force is applied, the body of mass m moves with uniform velocity.

Hence, Newton's first law of motion can be mathematically stated from the Newton's seconds law.


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