Calculating The Center of Percussion
For a free, rigid beam, a force F applied at right angle at a distance b from the center of gravity (CoG) will result in the CoG moving at a velocity V according to the relation:
where M is the mass of the beam. Similarly the torque exerted will be as per the relation:
where I is the moment of inertia around the CoG and is the angular velocity.
For any point P on the opposite side of the CoG from the point of impact, the velocity of point P is
where A is the distance of P from the CoG. Hence:
The velocity v is then given by:
The axis of rotation is situated where and the corresponding center of percussion is at distance b from the CoG, with
This is also the center of oscillation of a physical pendulum of the same mass M, hung at the pivot point. (The center of oscillation is the position of the mass of a simple pendulum that has the same period as the physical pendulum.)
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