Phys101-The_Physical_Universe

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 \(E\) & \(p\)

\[E^2=m_0^2c^4+p^2c^2\]