(a) What is $\gamma$ if v = 0.100c ? (b) If v = 0.900c ?

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to calculate the Lorentz factor that's the name for this thing... this γ, which equals 1 over the square root of 1 minus the relative velocity squared divided by the speed of light squared; we are going to calculate the value for γ given a speed of 0.100 times the speed of light c in part (a). So we have 1 over the square root of 1 minus 0.100c all squared divided by c squared and this c in the bracket becomes squared, which cancels with this c squared down here and we are left with 0.100 squared here and so we have 1 over the square root of 1 minus 0.100 squared, which is 1.00504. The value for γ when v is 0.900c is 1 over the square root of 1 minus 0.900 squared which is 2.294.