Question Video: Lorentz Factor Produced by a Relative Velocity | Nagwa Question Video: Lorentz Factor Produced by a Relative Velocity | Nagwa

Question Video: Lorentz Factor Produced by a Relative Velocity

What is the Lorentz factor 𝛾 produced by a relative velocity of 0.250𝑐?

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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.

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