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In the top picture, which is how torque is typically explained, the center of rotation is different than in the bottom picture. I think I understand how this works in the top picture, but I don't see how it translates to the bottom picture.

In the bottom picture (of a golf swing), the center of rotation of the club is around the hands, which are moving (actually, the center of rotation is above the hands because the hands are moving, but for simplicity, I think it's okay to assume the club shaft is rotating around the hands).

The problem for me is that I can't see how the centripetal force vector has any component that will accelerate the club head forward. So I can't see how the torque would be calculated.

Here are some typical numbers:

Torque: 50 Newton-meters, Centripetal force: 80 pounds, Club shaft length: 42 inches, Angle between the centripetal force vector and the shaft: 35 degrees.

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2 Answers 2

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The hands and wrist apply non-radial forces to the club handle. This is not a centripetal force; a centripetal force is radial. There is a force in the direction of the swing applied by the bottom hand, and a force in the opposite direction applied by the top hand. As the bottom hand is further from the hinge at the hands there is a resulting torque in the direction you have shown in your diagram 2.

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  • $\begingroup$ The force you are describing is call the hand-couple force. Each hand is pushing in the same direction as the torque and thus contributes to the torque. I should have mentioned that this force is very small and contributes very little to the acceleration of the swing. Imaging trying to just hold a club in your hands and accelerating it without actually making a swing with your body. You'd get very little acceleration. It's the centripetal force shown in the picture that produces most of the clubhead acceleration. Dave Tutleman has a website describing this. $\endgroup$
    – delusionist
    Commented Jun 9 at 4:49
  • $\begingroup$ Note that if we started with the club in the position shown (static without any golf swing) and then the butt of the club were pulled along the line of the centripetal force, the club would rotate in the direction of the torque shown until it lined up with the direction of the centripetal force. Of course, it would also move in the direction of the centripetal force. It doesn't do that in the golf swing because the inertial force of the clubhead moving in an arc essentially matches the centripetal force so he clubhead moves in an arc instead of along the line of the centripetal force. $\endgroup$
    – delusionist
    Commented Jun 9 at 4:58
  • $\begingroup$ Imagine that the hands were perfectly rigid. Then the force within the hands would be the force I described. However we would not analyse the motion as being circular motion about the hands but about the shoulder, and the work would come from gravity and the efforts of the upper arm and shoulder muscles. $\endgroup$
    – Peter
    Commented Jun 9 at 7:56
  • $\begingroup$ Imagine that the hands are hinges without muscles, but the hinge can be locked and unlocked. That approximates the golf swing. The early part of the swing, when the club is over the person's head, accelerates the club along an arc while the wrists are locked. Half way through the swing, the wrists unlock. The wrists/hinge begins to straighten because of the inertial force of the clubhead. As this happens, the body/arms react with centripetal force to keep the clubhead on an arc. That centripetal force, along with the tangential force of the body turning, accelerates the clubhead... $\endgroup$
    – delusionist
    Commented Jun 9 at 23:18
  • $\begingroup$ The tangential force of the body turning is small. The large force is the centripetal force (in my diagram above) that both keeps the clubhead on an arc and accelerates it. This is similar to swing a weight on the end of a rope around your body. The centripetal force accelerates the weight. In golf, that centripetal force is around 80-100 pounds (i.e. quite large) for a 120mph clubhead speed. $\endgroup$
    – delusionist
    Commented Jun 9 at 23:22
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The state object is in a differentiated matrix and it cannot be early club mechanics. Good centripetal force is in shaft and it cannot be objectified nicely.

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