Newton's Second Law Is Wrong! - Relativistic Momentum

Monday, October 08, 2018

Newton's Second Law Is Wrong! - Relativistic Momentum

Newton's 2nd law - F = ma

From this we get the equation for momentum
F = dp/dt
a = dv/dt

dp/dt = m dv/dt Integrating with respect to time then gives
p = mv
This is all WRONG.

Relativistic Momentum

In the post on relativistic mass, we saw that how hard it is to accelerate an object increases as its speed increases.
Below we will analyse a collision and attempt to derive the equation for relativistic momentum.

By using the momentum equation p = mvγ momentum is always conserved between frames.
You may see the equation in the form p = m_relγ as some people use relativistic mass as a concept but we discussed why this isn't ideal in the last post.

Differentiating both sides of the equation with respect to time will give the real version of F=ma.

From this new equation for momentum we can go on to derive the relativistic kinetic energy formula. This will be the last tool we need to take on E = mc².

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