Phys101-The_Physical_Universe

Table of Contents

  1. Special Relativity
    1. Time Dilation
    2. Length Contraction
    3. Relativistic Momentum
    4. Relativistic Energy
    5. Kinetic Energy
    6. Linking $E$ & $p$

The majority of PHYS101 is covered at A Level, so I have only covered the new content (special relativity) in this module summary.

Special Relativity

Time Dilation

$$\Delta t=\frac{\Delta t_0}{\sqrt{1-\frac{u^2}{c^2}}},\;\;\; \beta=\frac{u}{c},\;\;\;\Delta t = \gamma\Delta t_0$$

Length Contraction

$$l=\frac{l_0}{\sqrt{1-\beta^2}},\;\;\;\beta=\frac{u}{c},\;\;\;l_0=\gamma l$$

Relativistic Momentum

$p=mv$ applies if $m$ is the objects relativistic mass $(m=\gamma m_0)$, otherwise: $$p=\frac{m_0v}{\sqrt{1-\frac{u^2}{c^2}}}=\gamma m_0v$$

Relativistic Energy

$$E=\gamma m_0c^2=mc^2$$

Kinetic Energy

$$K=(\gamma -1)m_0c^2$$

Linking $E$ & $p$

$$E^2=m_0^2c^4+p^2c^2$$