1. The problem statement, all variables and given/known data Find the total tension acting on a rod rotating about its end with an angular velocity of w as a function of its length x(length) 2. Relevant equations F = ma 3. The attempt at a solution Let the function be T(x) where x is the length of the rod. Considering an interval between x and x + dx For an increment in dx, let the function change by dT(x) dT(x) = T(x+dx) - T(x) T(x+dx) is the tension acting on a rod of length x + dx T(x) is the tension acting on a rod of length x Therefore, dT(x) is the tension acting on the tiny element of length dx dT(x) = dm(w^2) x dm = ρdx ∫dT(x) = ρ(w^2)∫ xdx from T(x) = 0 at x = 0 to T(x) at x = x. This gives me tension as a function of the length of the rod Is what I've done correct & rigorous? Is my general approach to calculus alright or am I viewing things wrong?