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timza

Imagine a moving rigid body B1 like a golf clubhead impacts with a stationary elastic body B2 like a golfball. Imagine that the initial velocity of the golfball at time T1 is zero, and the final velocity of the golf ball at time T2 is some value. Imagine that time T1 is when the clubhead first strikes the elastic golfball, and time T2 is when the elastic golf ball has retained its round shape and leaves the clubhead. Imagine we can know what the moment of inertia and angular velocity is of the golfer/shaft/clubhead system B1 at T1. I realize that I just kind of threw in a wrench when I then spoke of B1 as not just being a clubhead, but instead now a system of golfer/shaft/clubhead. But the face of the clubhead is rigid.

Question: For three scenarios, where the clubhead velocity at T1 is exactly the same for each scenario, is the resultant final velocity of the golfball B2 greater, the same, or lesser, if at impact time T1 the clubhead B1 is: 1. moving at a constant velocity, 2. increasing in velocity (accelerating), or 3. decreasing in velocity (decelerating)?

If I knew the moment of inertia and the angular velocity of the golfer/shaft/clubhead B1, at impact time T1 I would know the initial momentum of the collision because the golfball B2 is at rest and has zero momentum. So then if I knew the mass of the golf ball and assumed flush contact and linear momentum, and no golfball spin after impact, I could use the conservation of momentum to find the final golfball velocity at time T2. But I think that the conservation of momentum is based on both bodies under constant speed.

If I wanted to calculate the force during the deformation of the elastic ball I could video the impact and measure the time between the start of the impact at time T1 to the release of the ball at time T2, and impulse equals force times delta time equals mass times change in velocity. I have my change in golfball velocities from the above conservation of momentum, and now I have the change in time, so I could find my force.

But, if the clubhead was accelerating at the start of impact at time T1, I would say that there was/is a force that was/is continuing to act on that shaft/clubhead system through impact. So back to the impulse equation. Now I could assume that since the golfer/shaft/clubhead is accelerating at T1 that the force that causes the accelerating continues through impact, and add that force to the impulse equation, to find a new, greater final velocity of the ball at time T2.

Whew. Where am I wrong? Is there a different equation that I don't even know enough about to Google for that would involve Initial and Final accelerations during impact, or involve an additional constant force through impact? I do not need to calculate actual numbers. I just want to study and learn the concepts.

I have for years talked to golfers who have just enough knowledge of physics to believe that golfball impact is only about the velocity of the clubhead and the force to the golf ball. They live in an F = ma world and often believe that if you cut the clubhead from the system of the golfer/shaft right before impact the distance the ball would go would be the same as if the clubhead remained connected to the golfer/shaft. They do not agree with me that you can increase the moment of inertia of the golfer/shaft/clubhead system to increase final golfball velocity after impact, even at the same measured clubhead velocity. But now I am thinking that I have been missing something in the force that the golfer continues to apply to the shaft/clubhead at and through impact.

Thank you. First time post. My searching led me to this forum. But I did not find anything specific on these concepts.

Question: For three scenarios, where the clubhead velocity at T1 is exactly the same for each scenario, is the resultant final velocity of the golfball B2 greater, the same, or lesser, if at impact time T1 the clubhead B1 is: 1. moving at a constant velocity, 2. increasing in velocity (accelerating), or 3. decreasing in velocity (decelerating)?

If I knew the moment of inertia and the angular velocity of the golfer/shaft/clubhead B1, at impact time T1 I would know the initial momentum of the collision because the golfball B2 is at rest and has zero momentum. So then if I knew the mass of the golf ball and assumed flush contact and linear momentum, and no golfball spin after impact, I could use the conservation of momentum to find the final golfball velocity at time T2. But I think that the conservation of momentum is based on both bodies under constant speed.

If I wanted to calculate the force during the deformation of the elastic ball I could video the impact and measure the time between the start of the impact at time T1 to the release of the ball at time T2, and impulse equals force times delta time equals mass times change in velocity. I have my change in golfball velocities from the above conservation of momentum, and now I have the change in time, so I could find my force.

But, if the clubhead was accelerating at the start of impact at time T1, I would say that there was/is a force that was/is continuing to act on that shaft/clubhead system through impact. So back to the impulse equation. Now I could assume that since the golfer/shaft/clubhead is accelerating at T1 that the force that causes the accelerating continues through impact, and add that force to the impulse equation, to find a new, greater final velocity of the ball at time T2.

Whew. Where am I wrong? Is there a different equation that I don't even know enough about to Google for that would involve Initial and Final accelerations during impact, or involve an additional constant force through impact? I do not need to calculate actual numbers. I just want to study and learn the concepts.

I have for years talked to golfers who have just enough knowledge of physics to believe that golfball impact is only about the velocity of the clubhead and the force to the golf ball. They live in an F = ma world and often believe that if you cut the clubhead from the system of the golfer/shaft right before impact the distance the ball would go would be the same as if the clubhead remained connected to the golfer/shaft. They do not agree with me that you can increase the moment of inertia of the golfer/shaft/clubhead system to increase final golfball velocity after impact, even at the same measured clubhead velocity. But now I am thinking that I have been missing something in the force that the golfer continues to apply to the shaft/clubhead at and through impact.

Thank you. First time post. My searching led me to this forum. But I did not find anything specific on these concepts.

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