1. The problem statement, all variables and given/known data In a laboratory, a pion moves in a circular orbit of radius r and period T as measured in the lab frame. How much proper time elapses during one revolution as seen by the pion? 2. Relevant equations Let period = T Let radius = r Let v = velocity (1) v = (2 * pi * r) / T Equation of time dilation (2) T(proper time) = T / gamma where gamma is the usual Lorentz factor 3. The attempt at a solution This is an accelerated problem since the velocity of the pion particle is constantly changing (well, it's direction). I tried to plug in equation (1) into equation (2) but I realised gamma is not constant since the velocity is changing.... so how should I approach this problem. Help! Thank you!