What properties/equations prove that a golf club that is longer in length (everything else constant, mass, torque at grip, etc.) will have more club head speed or more kinectic energy that one of shorter length? Thanks for the help.
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It's the connection between rotational motion and circular motion. If (circular motion)
and the whole body has the same angular velocity, then by the definition of circular tangential velocity, a circle with a larger radius has to have a faster velocity at the circumference. Think about record player...a point at the edge has to move faster than a point nearer the center in order for it to have the same angular velocity.