When swinging at a golf ball, the objective is to strike the ball
in the center of the club head commonly known as the "sweet spot".
Inevitably, golf balls will be struck off center and an interesting
physics situation occurs.
A perfectly hit ball creates an enormous amount of backspin, approximately
3500 rpm. To achieve this, the ball while it is in contact with the
club for 0.5 ms must obtain a pure rolling motion. What happens if
the ball is not hit in the center?
If the ball were hit off center and the ball is rolling on the club
face we might expect it to spin in the opposite direction, clockwise
in figure 1. This is not the case, since the club puts a large force
on the ball, by Newton's third law, the ball puts a large force on
the club ~17500 N. This force rotates the club head in the direction
of "F x r". Therefore the ball in this brief impact rolls
producing a spin in the opposite direction.
If the club face were flat, every golf shot hit off center would
not find it's way into the fairway, but since it is convex the path
will initially travel in a direction normal to the club face and curve
back into the fairway.
Penner5 finds that the optimum radius of curvature of
a club face for a 200g driver should be 21.5 cm. Increasing the mass
would increase the curvature.