Circular motion when the gymnast is spinning, tension and torque when the gymnast is using ropes, potential and kinetic energy when the gymnast is holding a position in the air and then moves, turning about a pivot when the gymnast is balancing, kinematics for the movement of the gymnast (i guess it's a bit of an over simplification to treat her/him as a particle though)...just some ideas i know some of these concepts may be thought to relate more to physics than maths but lots of equations come into play.