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.