EINSTEIN / NEWTON

Following on from Einstein's theory of relativity some teachers of science have suggested that Newton got it wrong. He did not!

Newton's second law of motion is mathematically represented by the equation F = d(mv)/dt.
 Not F = ma. Newton assumed that if an object is subjected to an unbalanced force its inertial mass m would not change and that F = d(mv)/dt would simplify down to F = ma. For velocities of say 100m/s changes in inertial mass are not measurable.

Einstein took Newton's second law from one inertial reference frame (which is one in which Newton's second law holds) to another such frame using Lorentz transformations. When this was done he found that for the law to hold (Galilean Invariance) the objects inertial mass changed. The new mass is represented by the equation m = m' /w, where w = square root (1 - v.v/c,c) and m' is the objects inertial mass in the rest frame.

This is Einstein's only modification of Newton's laws of motion. Newton's first law remains unchanged. Newton's third law still holds but the modified mass must now be taken into account when considering conservation of momentum.