Video Transcript
What is the Lorentz factor 𝛾
produced by a relative velocity of 0.250𝑐?
We can call that relative
velocity, 0.250𝑐, 𝑣. And we want to solve in this
exercise for the Lorentz factor, 𝛾. To do that, we can recall the
mathematical form for this term. 𝛾 is defined as one divided by
the square root of one minus 𝑣 squared over 𝑐 squared. In our case, we’ve been told
the velocity 𝑣. So we’re ready to plug in at
this equation to solve for 𝛾. When we do, we see under the
square root sign that the factors of the speed of light 𝑐 cancel out,
simplifying our denominator. When we enter this value on our
calculator to solve for 𝛾, we find that, to three significant figures, it’s
1.03. So even when our speed is a
quarter of the speed of light, 𝛾 is only slightly above one.