Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems General Relativity: An Introduction for Physicists · Problem 5.22
Special relativity revisited — Hobson, Efstathiou & Lasenby
Physics · free-particle-rotating-cylindrical-coordinates
Problem Repeat Exercise 5.21 for the coordinates ( c t , ρ , ϕ , z ) (ct, \rho, \phi, z) ( c t , ρ , ϕ , z ) ( c T , X , Y , Z ) (cT, X, Y, Z) ( c T , X , Y , Z ) T = t , X = ρ cos ϕ cos ω t − ρ sin ϕ sin ω t , Y = ρ cos ϕ sin ω t + ρ sin ϕ cos ω t , Z = z , \begin{aligned}
T &= t,\\
X &= \rho\cos\phi\cos\omega t - \rho\sin\phi\sin\omega t,\\
Y &= \rho\cos\phi\sin\omega t + \rho\sin\phi\cos\omega t,\\
Z &= z,
\end{aligned} T X Y Z = t , = ρ cos ϕ cos ω t − ρ sin ϕ sin ω t , = ρ cos ϕ sin ω t + ρ sin ϕ cos ω t , = z , ω \omega ω Browse the problem library