1. The problem statement, all variables and given/known data A particle is at rest at the apex A of a smooth fixed hemisphere whose base is horizontal. The hemisphere has centre O and radius a. The particle is then displaced very slightly from rest and moves on the surface of the hemisphere. At the point P on the surface where angle AOP = α the particle has speed v. Find an expression for v in terms of a, g and α. 2. Relevant equations 3. The attempt at a solution So I’ve worked like this: Total energy at A = PE + KE = amg + 0 Total energy at P = PE + KE = (0.5m(v^2)) + xmg x = a – y (cos α)/y = (sin90)/a => y = a(cos α) => x = a – (a(cos α)) = a (1 - cos α) => Total energy at P = PE + KE = (0.5m(v^2)) + amg (1 - cos α) Therefore (Total energy at A) = (Total energy at P) gives amg = (0.5m(v^2)) + amg (1 - cos α) ag = 0.5(v^2) + ag (1 – cos α) ag – ag (1 – cos α) = 0.5(v^2) 2ag (1 – 1 + cos α) = v^2 v = sqrt (2ag (cos α)) However, the correct answer is v = sqrt (2ag (1 - cos α)) Where’s the problem?