Biomechanics of the Vaulter
When you add the torque due to gravity, the angular velocity of the center of mass of the pole can be determined. At the top of the jump, the torque due to gravity and the torque associated with the force of the vaulter are zero because their force orientations are parallel with the pole and intersect the axis of rotation. The quadriceps contract with a great force at take-off, providing the vertical lift, and thus torque on the pole, necessary to reach a maximum height. (This is the reason why my tibial tuberosity broke off during that one jump. The fact that it tore off compromised my ability to divert momentum into a vertical direction, so all of my momentum was put into bending the pole. The number one rule in pole vaulting is to never let go of the pole when something goes awry, otherwise this happens, so the pole bent past the 110º limit and snapped into 5 pieces — pretty cool.)
The force exerted by the pole on the vaulter can be seen as a constant, spring force. The stiffness of the pole (provided by the spring constant, k) determines the force that the pole is able to exert back on to the vaulter. A component of this force acts as a torque on the vaulter’s center of mass, causing the body to rotate 180º to end up at a vertical position. The best vaulters try to position their center of mass almost directly above the axis of rotation for as long as possible during the ascent in order to maximize the vertical component of the work exerted by the unbending of the pole.
The vaulter’s arms are extended and held in that position for the take-off. The vaulter then pulls their body up as their horizontal velocity is decreasing. They then extend their arms again at the peak of the vault in order to experience an additional upward normal force.
Here is a .gif that may help explain the body position progression:
That is all.