Special Relativity

Question 1

Give the equations for the Lorentz transformations

Answer 1

Question 2

Give the equations for the Lorentz transformations in terms of γ

Answer 2

Question 3

Give the inverse Lorentz equation’s matrix

Answer 3

Question 4

Give the equation for L, the length of a moving object moving along an axis

Answer 4

Question 5

Give an equation for L, the length of a moving object which is moving at an angle to the x-axis

Answer 5

Question 6

Give the equations relating the velocity of an object observed in two systems

Answer 6

Note that x,y,z and t can be swapped for x’,y’,z’ and t’ and the velocity’s sign changed for the transformations the opposite way.

Question 7

Define γ, The Lorentz factor

Answer 7

Question 8

Give the equation for T₁, the time between the arrival of pulses at the observer

Answer 8

Note that T0 is the time interval between pulses

Question 9

Give the equation for f, the frequency of light received by the observer

Answer 9

Note that f₀ is 1/T₀

Question 10

Give the equation for λ, the wavelength of the source seen by the observer

Answer 10

Note that λ₀ = c/f₀

Question 11

Give the frequency of a source if the source is moving perpendicular to the line between it and the observer

Answer 11

Question 12

Give the relativistic expression for momentum

Answer 12

Question 13

Give the relativistic equation for kinetic energy

Answer 13

Question 14

Express the formula for total energy in terms of momentum

Answer 14

Question 15

State the energy-momentum four-vector

Answer 15

Question 16

Give the equation for energy for a massless particle

Answer 16

Note: for E and p to both not equal zero, the particle must be travelling at the speed of light

Question 17

State the rest energy of a stationary body

Answer 17

mc²