The Physics of Power: How Angular Momentum Shapes the Tennis Forehand

[stroke]

so you mean in the transition from backswing to forward swing?

Not in the transition. There is a point just before the forward move of the hand to the ball that the wrist goes to neutral. That is the case on the ATP forehand whether the wrist is extended in the unit turn or not. If the wrist stays extended during the entire motion, from the unit turn on, it is basically the WTA type forehand.

[stroke]

It’s not about having the ‘biggest’ it's about ‘efficiency’. It’s about a player adopting a functional backswing versus a positional backswing. The two best forehands ever thus far are Rafa’s and Roger’s – both positional. A functional backswing is going to involve more work to produce the same thing.

Wholeheartedly agree, Nadal and Fed the number 1 and 2 forehands ever to me. They are so similar, as BG pointed out years ago(before anyone else). Nadal just does everything Fed does to an extreme to produce the ball he did.

[clewit]

Sorry guys, I accidentally deleted this thread. Airforce1 had a comment about the article being biased towards the straight armed forehand, and that a bent arm can produce just as much power. If you watch Sinner, with his bent arm, for just a minute you can see how he obliterates the ball. So I would argue that you can get just as much angular momentem with the bent armed forehand, but some of the physics changes with the length of the lever. I'll leave it to Chris though.

thank you guys. Sorry. My account would not allow posting until Jeff fixed it.

Here are a few thoughts:

In tennis, speed is power, and what matters most is racket head speed at the point of contact, not just raw mechanical force.

When a player like Roger Federer extends the arm, it doesn’t necessarily increase angular velocity. In fact, it can reduce it—because extending the arm increases the moment of inertia, or the resistance to rotation. However, it can increase total angular momentum, which is what ultimately matters when transferring energy through the kinetic chain.

This concept comes from the equation:

L = I x w

In this equation:
• L is angular momentum
• I is moment of inertia
• w (omega) is angular velocity, or the rate of rotation in radians per second

Even though omega may decrease due to the increased length of the lever, I (moment of inertia) increases substantially as mass is distributed farther from the axis of rotation (e.g., the shoulder). This can result in greater overall angular momentum, which helps generate high racket head speed when efficiently transferred through the kinetic chain.

Biomechanics researcher Dr. Brian Gordon has also hypothesized that the straight-arm forehand configuration—where the hitting arm is extended beyond 155 degrees—can contribute to producing a heavier ball. The reasoning is that this configuration allows for a greater contribution from internal shoulder rotation (ISR), which is the dominant source of racket head speed in the modern forehand. By maximizing ISR contribution, players may increase spin rate and momentum transfer to the ball, resulting in a shot that combines pace and heavy topspin.

This becomes especially effective when the full kinetic chain—starting from the ground and moving through the hips, torso, shoulder, arm, and wrist—is sequenced correctly. The result is a whip-like effect that generates maximum speed at the point of contact, even without an increase in torque at the shoulder.

Let’s continue the discussion—happy to explore the implications of ISR, angular momentum, and forehand configurations in more detail.

So my observation is that great players are extending their arm for the forehand to generate more angular momentum but also to generate higher spin rates.

[clewit]

In the wooden racket days, no one could conceive that anyone would have so much angular motion that players would some day spin off their front or rear foot and even leave the ground. Perhaps we might all someday witness a 360 degree followthrough!

Yes!

[clewit]

Jeffrey’s comment brings to mind something I’ve wondered about within the bent v straight arm forehand discussion. I’m not a mechanical engineer but I wonder if there is an element missing in the analysis. Let’s grant the basic idea that, given a particular angular velocity, i.e., greater speed of rotation, there is a mechanical advantage to a longer lever because the tip speed will be higher. This is basic high school physics.

But, is it possible that players who use a bent arm can generate more angular velocity because it takes less effort to do this with a shorter lever? If you look at some great players with very bent arms on the FH, e.g., Sam Querry, Jack Sock, Nick Kyrios, Osaka when she was winning, Iga, Goran Ivanisevic, it always looks to me like they rotate unbelievably quickly and get very high racquet speeds. To look at a classic example of this in another sport, consider a classic figure skater’s spin. The spin typically starts with the arms fully outstretched horizontally and then as the skater brings the arms up over the head, thereby shortening the lever, the body rotates faster and faster.

This idea would suggest there might be a trade-off where a player with a bent arm can rotate the torso faster and generate equal tip speed to a player with a straight arm who is rotating a bit more slowly but getting the same speed through a longer lever.

Chris Lewitt, if you’re listening, we’d love to hear from you!

Thanks. This is a great comment. Good discussion. I added these thoughts:

In tennis, speed is power, and what matters most is racket head speed at the point of contact, not just raw mechanical force.

When a player like Roger Federer extends the arm, it doesn’t necessarily increase angular velocity. In fact, it can reduce it—because extending the arm increases the moment of inertia, or the resistance to rotation. However, it can increase total angular momentum, which is what ultimately matters when transferring energy through the kinetic chain.

This concept comes from the equation:

L = I x w

In this equation:
• L is angular momentum
• I is moment of inertia
• w (omega) is angular velocity, or the rate of rotation in radians per second

Even though omega may decrease due to the increased length of the lever, I (moment of inertia) increases substantially as mass is distributed farther from the axis of rotation (e.g., the shoulder). This can result in greater overall angular momentum, which helps generate high racket head speed when efficiently transferred through the kinetic chain.

Biomechanics researcher Dr. Brian Gordon has also hypothesized that the straight-arm forehand configuration—where the hitting arm is extended beyond 155 degrees—can contribute to producing a heavier ball. The reasoning is that this configuration allows for a greater contribution from internal shoulder rotation (ISR), which is the dominant source of racket head speed in the modern forehand. By maximizing ISR contribution, players may increase spin rate and momentum transfer to the ball, resulting in a shot that combines pace and heavy topspin.

This becomes especially effective when the full kinetic chain—starting from the ground and moving through the hips, torso, shoulder, arm, and wrist—is sequenced correctly. The result is a whip-like effect that generates maximum speed at the point of contact, even without an increase in torque at the shoulder.

Let’s continue the discussion—happy to explore the implications of ISR, angular momentum, and forehand configurations in more detail.

So my observation is that great players are extending their arm for the forehand to generate more angular momentum but also to generate higher spin rates.

[clewit]

Jeffrey’s comment brings to mind something I’ve wondered about within the bent v straight arm forehand discussion. I’m not a mechanical engineer but I wonder if there is an element missing in the analysis. Let’s grant the basic idea that, given a particular angular velocity, i.e., greater speed of rotation, there is a mechanical advantage to a longer lever because the tip speed will be higher. This is basic high school physics.

But, is it possible that players who use a bent arm can generate more angular velocity because it takes less effort to do this with a shorter lever? If you look at some great players with very bent arms on the FH, e.g., Sam Querry, Jack Sock, Nick Kyrios, Osaka when she was winning, Iga, Goran Ivanisevic, it always looks to me like they rotate unbelievably quickly and get very high racquet speeds. To look at a classic example of this in another sport, consider a classic figure skater’s spin. The spin typically starts with the arms fully outstretched horizontally and then as the skater brings the arms up over the head, thereby shortening the lever, the body rotates faster and faster.

This idea would suggest there might be a trade-off where a player with a bent arm can rotate the torso faster and generate equal tip speed to a player with a straight arm who is rotating a bit more slowly but getting the same speed through a longer lever.

Chris Lewitt, if you’re listening, we’d love to hear from you!

Thoughtful comments. It all comes down to mathematics.

Here are a few thoughts:

In tennis, speed is power, and what matters most is racket head speed at the point of contact, not just raw mechanical force.

When a player like Roger Federer extends the arm, it doesn’t necessarily increase angular velocity. In fact, it can reduce it—because extending the arm increases the moment of inertia, or the resistance to rotation. However, it can increase total angular momentum, which is what ultimately matters when transferring energy through the kinetic chain.

This concept comes from the equation:

L = I x w

In this equation:
• L is angular momentum
• I is moment of inertia
• w (omega) is angular velocity, or the rate of rotation in radians per second

Even though omega may decrease due to the increased length of the lever, I (moment of inertia) increases substantially as mass is distributed farther from the axis of rotation (e.g., the shoulder). This can result in greater overall angular momentum, which helps generate high racket head speed when efficiently transferred through the kinetic chain.

Biomechanics researcher Dr. Brian Gordon has also hypothesized that the straight-arm forehand configuration—where the hitting arm is extended beyond 155 degrees—can contribute to producing a heavier ball. The reasoning is that this configuration allows for a greater contribution from internal shoulder rotation (ISR), which is the dominant source of racket head speed in the modern forehand. By maximizing ISR contribution, players may increase spin rate and momentum transfer to the ball, resulting in a shot that combines pace and heavy topspin.

This becomes especially effective when the full kinetic chain—starting from the ground and moving through the hips, torso, shoulder, arm, and wrist—is sequenced correctly. The result is a whip-like effect that generates maximum speed at the point of contact, even without an increase in torque at the shoulder.

Let’s continue the discussion—happy to explore the implications of ISR, angular momentum, and forehand configurations in more detail.

So my observation is that great players are extending their arm for the forehand to generate more angular momentum but also to generate higher spin rates.

[clewit]

Jeffrey’s comment brings to mind something I’ve wondered about within the bent v straight arm forehand discussion. I’m not a mechanical engineer but I wonder if there is an element missing in the analysis. Let’s grant the basic idea that, given a particular angular velocity, i.e., greater speed of rotation, there is a mechanical advantage to a longer lever because the tip speed will be higher. This is basic high school physics.

But, is it possible that players who use a bent arm can generate more angular velocity because it takes less effort to do this with a shorter lever? If you look at some great players with very bent arms on the FH, e.g., Sam Querry, Jack Sock, Nick Kyrios, Osaka when she was winning, Iga, Goran Ivanisevic, it always looks to me like they rotate unbelievably quickly and get very high racquet speeds. To look at a classic example of this in another sport, consider a classic figure skater’s spin. The spin typically starts with the arms fully outstretched horizontally and then as the skater brings the arms up over the head, thereby shortening the lever, the body rotates faster and faster.

This idea would suggest there might be a trade-off where a player with a bent arm can rotate the torso faster and generate equal tip speed to a player with a straight arm who is rotating a bit more slowly but getting the same speed through a longer lever.

Chris Lewitt, if you’re listening, we’d love to hear from you!

thank you guys. Sorry. My account would not allow posting until Jeff fixed it.

Here are a few thoughts:

In tennis, speed is power, and what matters most is racket head speed at the point of contact, not just raw mechanical force.

When a player like Roger Federer extends the arm, it doesn’t necessarily increase angular velocity. In fact, it can reduce it—because extending the arm increases the moment of inertia, or the resistance to rotation. However, it can increase total angular momentum, which is what ultimately matters when transferring energy through the kinetic chain.

This concept comes from the equation:

L = I x w

In this equation:
• L is angular momentum
• I is moment of inertia
• w (omega) is angular velocity, or the rate of rotation in radians per second

Even though omega may decrease due to the increased length of the lever, I (moment of inertia) increases substantially as mass is distributed farther from the axis of rotation (e.g., the shoulder). This can result in greater overall angular momentum, which helps generate high racket head speed when efficiently transferred through the kinetic chain.

Biomechanics researcher Dr. Brian Gordon has also hypothesized that the straight-arm forehand configuration—where the hitting arm is extended beyond 155 degrees—can contribute to producing a heavier ball. The reasoning is that this configuration allows for a greater contribution from internal shoulder rotation (ISR), which is the dominant source of racket head speed in the modern forehand. By maximizing ISR contribution, players may increase spin rate and momentum transfer to the ball, resulting in a shot that combines pace and heavy topspin.

This becomes especially effective when the full kinetic chain—starting from the ground and moving through the hips, torso, shoulder, arm, and wrist—is sequenced correctly. The result is a whip-like effect that generates maximum speed at the point of contact, even without an increase in torque at the shoulder.

Let’s continue the discussion—happy to explore the implications of ISR, angular momentum, and forehand configurations in more detail.

So my observation is that great players are extending their arm for the forehand to generate more angular momentum but also to generate higher spin rates.

[clewit]

Jeffrey’s comment brings to mind something I’ve wondered about within the bent v straight arm forehand discussion. I’m not a mechanical engineer but I wonder if there is an element missing in the analysis. Let’s grant the basic idea that, given a particular angular velocity, i.e., greater speed of rotation, there is a mechanical advantage to a longer lever because the tip speed will be higher. This is basic high school physics.

But, is it possible that players who use a bent arm can generate more angular velocity because it takes less effort to do this with a shorter lever? If you look at some great players with very bent arms on the FH, e.g., Sam Querry, Jack Sock, Nick Kyrios, Osaka when she was winning, Iga, Goran Ivanisevic, it always looks to me like they rotate unbelievably quickly and get very high racquet speeds. To look at a classic example of this in another sport, consider a classic figure skater’s spin. The spin typically starts with the arms fully outstretched horizontally and then as the skater brings the arms up over the head, thereby shortening the lever, the body rotates faster and faster.

This idea would suggest there might be a trade-off where a player with a bent arm can rotate the torso faster and generate equal tip speed to a player with a straight arm who is rotating a bit more slowly but getting the same speed through a longer lever.

Chris Lewitt, if you’re listening, we’d love to hear from you!

Great comment.

But here’s the nuance: in tennis, speed is power, and what matters most is racket head speed at the point of contact, not just raw mechanical force.

When a player like Roger Federer extends the arm, it doesn’t necessarily increase angular velocity. In fact, it can reduce it—because extending the arm increases the moment of inertia, or the resistance to rotation. However, it can increase total angular momentum, which is what ultimately matters when transferring energy through the kinetic chain.




This concept comes from the equation:




L = I x w




In this equation:

• L is angular momentum
• I is moment of inertia
• w (omega) is angular velocity, or the rate of rotation in radians per second

Even though \omega may decrease due to the increased length of the lever, I (moment of inertia) increases substantially as mass is distributed farther from the axis of rotation (e.g., the shoulder). This can result in greater overall angular momentum, which helps generate high racket head speed when efficiently transferred through the kinetic chain.




Biomechanics researcher Dr. Brian Gordon has also hypothesized that the straight-arm forehand configuration—where the hitting arm is extended beyond 155 degrees—can contribute to producing a heavier ball. The reasoning is that this configuration allows for a greater contribution from internal shoulder rotation (ISR), which is the dominant source of racket head speed in the modern forehand. By maximizing ISR contribution, players may increase spin rate and momentum transfer to the ball, resulting in a shot that combines pace and heavy topspin.

This becomes especially effective when the full kinetic chain—starting from the ground and moving through the hips, torso, shoulder, arm, and wrist—is sequenced correctly. The result is a whip-like effect that generates maximum speed at the point of contact, even without an increase in torque at the shoulder.


Let’s continue the discussion—happy to explore the implications of ISR, angular momentum, and forehand configurations in more detail.

[don_budge]

Thoughtful comments. It all comes down to mathematics.

Here are a few thoughts:

In tennis, speed is power, and what matters most is racket head speed at the point of contact, not just raw mechanical force.

When a player like Roger Federer extends the arm, it doesn’t necessarily increase angular velocity. In fact, it can reduce it—because extending the arm increases the moment of inertia, or the resistance to rotation. However, it can increase total angular momentum, which is what ultimately matters when transferring energy through the kinetic chain.

This concept comes from the equation:

L = I x w

In this equation:
• L is angular momentum
• I is moment of inertia
• w (omega) is angular velocity, or the rate of rotation in radians per second

Even though omega may decrease due to the increased length of the lever, I (moment of inertia) increases substantially as mass is distributed farther from the axis of rotation (e.g., the shoulder). This can result in greater overall angular momentum, which helps generate high racket head speed when efficiently transferred through the kinetic chain.

Biomechanics researcher Dr. Brian Gordon has also hypothesized that the straight-arm forehand configuration—where the hitting arm is extended beyond 155 degrees—can contribute to producing a heavier ball. The reasoning is that this configuration allows for a greater contribution from internal shoulder rotation (ISR), which is the dominant source of racket head speed in the modern forehand. By maximizing ISR contribution, players may increase spin rate and momentum transfer to the ball, resulting in a shot that combines pace and heavy topspin.

This becomes especially effective when the full kinetic chain—starting from the ground and moving through the hips, torso, shoulder, arm, and wrist—is sequenced correctly. The result is a whip-like effect that generates maximum speed at the point of contact, even without an increase in torque at the shoulder.

Let’s continue the discussion—happy to explore the implications of ISR, angular momentum, and forehand configurations in more detail.

So my observation is that great players are extending their arm for the forehand to generate more angular momentum but also to generate higher spin rates.

In tennis...speed is one element of control, which is power. The other two are spin and placement.

[stotty]

My question to Chris and other posters would be:

From a biomechanical standpoint, when executing a one-handed topspin backhand, which stance is more conducive to generating maximum racket head speed and power — a neutral stance or a closed stance?

Maybe this helps to visualize your question: In fast pitch softball most batters do not go past a neutral stance because of timing difficulty in making contact. In slow pitch softball many batters go well past a neutral stance to increase angular momentum and "swing for the fence". Their back almost faces the pitcher. My guess would be a closed stance generates more head speed.

You’d think so when you study the science but I’m not too sure. A player can get a deeper turn and unwind more with a closed stance but then the hips must act as a block at a certain point —whereas a neutral stance allows freer hip rotation and for the contact to be more in front. I spoke to a number of players with high level backhands (I don’t) and they all say the neutral stance gives them a bit more juice. If in doubt, ask the players.

[stroke]

https://youtu.be/pQ793MBQE50?si=Y8QLQvv8Ug1bK98R

This to me a great lesson the one hander, where he addresses the strongest contact point. I would say from this, if he is correct about the "upper back" being the strongest muscles that one should seek to access on the one hander, it would be the closed stance.

[stroke]

https://youtu.be/wVa4XQPcaqs?si=rLuN0kwEwApHEUHX

Here is another related lesson on this ideal contact point. You can really see how he naturally sets up in a closed stance on the backhand demonstration.

[hybridfh]

My question to Chris and other posters would be:

From a biomechanical standpoint, when executing a one-handed topspin backhand, which stance is more conducive to generating maximum racket head speed and power — a neutral stance or a closed stance?



You’d think so when you study the science but I’m not too sure. A player can get a deeper turn and unwind more with a closed stance but then the hips must act as a block at a certain point —whereas a neutral stance allows freer hip rotation and for the contact to be more in front. I spoke to a number of players with high level backhands (I don’t) and they all say the neutral stance gives them a bit more juice. If in doubt, ask the players.

Closed stance generates more power, from the greater left hip loading (I also feel that that greater loading gives my hips more runway before transferring the energy to my arm). And actually Hugh Clarke - Thread of Order guy - touched on this recently in his write-up on the Tsitsipas backhand. He said Tsitsipas doesn't use the closed stance nearly often enough.

[stotty]

Closed stance generates more power, from the greater left hip loading (I also feel that that greater loading gives my hips more runway before transferring the energy to my arm). And actually Hugh Clarke - Thread of Order guy - touched on this recently in his write-up on the Tsitsipas backhand. He said Tsitsipas doesn't use the closed stance nearly often enough.

Great post and thanks for your input. There are lot of different opinions over this one. That’s why I put it out there.

My argument would be a closed stance involves placing more weight on the back foot, which makes it harder to transfer energy efficiently forward into the shot. With a neutral stance, a player can push off both legs more equally and use the ground to drive upward and forward through the kinetic chain. It’s always going to flow better and allows the hips and torso to uncoil more freely toward the net. And, of course, there is neutral and less neutral and a whole range of stances between.

[hybridfh]

Great post and thanks for your input. There are lot of different opinions over this one. That’s why I put it out there.

My argument would be a closed stance involves placing more weight on the back foot, which makes it harder to transfer energy efficiently forward into the shot. With a neutral stance, a player can push off both legs more equally and use the ground to drive upward and forward through the kinetic chain. It’s always going to flow better and allows the hips and torso to uncoil more freely toward the net. And, of course, there is neutral and less neutral and a whole range of stances between.

You're welcome and thanks for your perspective. I don't agree that the neutral stance's characteristic (which may or may not be true, I'm not sure) of allowing both legs to push "more equally" would help. Tennis power is primarily generated through rotation, not forward energy. It's rotational power channeled into the racket, through the kinetic chain, for a moment of forward impact. Closed stance allows more rotational energy to be stored and a bigger push off the rear leg. I think the rear leg contributes more power on any shot. On the forehand, it's about loading the rear leg; even when I hit my forehands out of a neutral stance (my preferred stance btw), it's the rear hip push and release which is driving most of the power, not the front leg....the rear leg energy gets channeled through the front leg but the energy is coming from the rear leg.