text: pendulum and energy? a pendulum is formed from a small ball of mass m on a string of length l. there is a peg of height h = l/3 above the pendulum's lowest point. from what minimum angle theta must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?  any ideas?   thanks i wish there was some way to include a drawing in the answers. starting from the end, we want the bob to complete a vertical circle about the peg. the radius of this circle will be l/3. the minimum velocity to complete the circle is given by v = sqrt (5*g*r) = sqrt (5*g*l/3). hence the ke of the bob at the lowest point is ke = 1/2 m*v^2 = 5/6 m*g*l.  this must be equal to the pe at the beginning of the swing. pe = m*g*l*(1 - cos theta). this gives cos theta = 1 - 5/6 = 1/6. thus the required angle = arccos 1/6 = 80.4 deg.  for the derivation of the min velocity for completion of a vertical circle, pl refer to any standard text book on mechanics.