I think I can rearrange the Lorentz contraction equation, solving for v using:
v=sqrt[1-(L/Lo)^2] x c^2
Would someone check my thinking please?
Thanks
v=sqrt[1-(L/Lo)^2] x c
Yes, you are correct in your thinking. To rearrange the Lorentz contraction equation to solve for velocity (v), you can follow these steps:
1. Start with the Lorentz contraction equation:
v = sqrt[1 - (L/Lo)^2] x c^2
2. Square both sides of the equation to get rid of the square root:
v^2 = [1 - (L/Lo)^2] x (c^2)^2
3. Expand the equation on the right-hand side:
v^2 = [1 - (L/Lo)^2] x c^4
4. Divide both sides of the equation by c^4:
v^2 / c^4 = [1 - (L/Lo)^2]
5. Rearrange the equation to solve for v:
v^2 = c^4 - (L/Lo)^2 x c^4
v = sqrt(c^4 - (L/Lo)^2 x c^4)
So, your rearranged equation is correct, and it allows you to calculate the velocity by plugging in the values for L (length observed) and Lo (rest length). Remember to use consistent units for length and the speed of light (c) in the equation.