> College of Science > Physics Dept > Tatsu Takeuchi > Special Relativity > Lecture Notes > Section 4
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4. Newton's Second Law

Newton's second law is an example of a law that is valid in all inertial frames. It says that if a force F is acting on an object of mass m, then its acceleration is proportional to F but inverse proportional to m. In other words

  1. the heavier the object is the harder it is to accelerate, and
  2. the harder you push the larger the acceleration will be.
Expressed as an equation, this would be

F = ma.

It is easy to see that if the law is correct in inertial frame A, then it is also correct in another inertial frame B.

This is because the relation

x' = x - vt,         t' = t

implies that the velocities of objects observed in frames A and B are related by

u' = u - v

which means that the acceleration is the same in both frames:

a' = a.

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