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Torque

Torque

Torque is an important quantity for describing the dynamics of a rotating rigid body. We see the application of torque in many ways in the world, such as when pressing the accelerator in a car, which causes the engine to apply additional torque on the drivetrain. Here, we define torque and provide a framework to create an equation to calculate torque for a rigid body with fixed-axis rotation.
Torque can be considered as the rotational counterpart to force. Since forces change the translational...

Relative Motion Analysis using Rotating Axes - Acceleration

Relative Motion Analysis using Rotating Axes - Acceleration

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...

Angular Velocity and Acceleration

Angular Velocity and Acceleration

We previously discussed angular velocity for uniform circular motion, however not all motion is uniform. Envision an ice skater spinning with their arms outstretched; when they pull their arms inward, their angular velocity increases. Additionally, think about a computer's hard disk slowing to a halt as the angular velocity decreases. The faster the change in angular velocity, the greater the angular acceleration. The instantaneous angular acceleration is defined as the derivative of angular...

Rotation with Constant Angular Acceleration - II

Rotation with Constant Angular Acceleration - II

Kinematics is the description of motion. The kinematics of rotational motion discusses the relationships between rotation angle, angular velocity, angular acceleration, and time. One can describe many things with great precision using kinematics, but kinematics does not consider causes. For example, a large angular acceleration describes a very rapid change in angular velocity without any consideration of its cause. Thus, rotational kinematics does not represent the laws of nature.
The first...

Equation of Rotational Dynamics

Equation of Rotational Dynamics

Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...

Relative Motion Analysis - Acceleration

Relative Motion Analysis - Acceleration

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...

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Related Experiment Video

Updated: Jul 16, 2026

Anterior Cruciate Ligament Transection and Synovial Fluid Lavage in a Rodent Model to Study Joint Inflammation and Posttraumatic Osteoarthritis

Anterior Cruciate Ligament Transection and Synovial Fluid Lavage in a Rodent Model to Study Joint Inflammation and Posttraumatic Osteoarthritis

Published on: September 2, 2025

The Torque-Velocity Relationship and Second ACL Injury Risk.

Xavier D Thompson¹, Amelia S Bruce Leicht², Jacob E Resch³

¹School of Kinesiology, Louisiana State University, Baton Rouge.

Journal of Athletic Training

|July 15, 2026

Summary

Patients who underwent anterior cruciate ligament reconstruction (ACLR) face high reinjury risks. The torque-velocity relationship can predict future ACL injuries, prompting closer monitoring of strong, young patients post-surgery.

Keywords:

injury prevention knee neuromuscular control

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Last Updated: Jul 16, 2026

Anterior Cruciate Ligament Transection and Synovial Fluid Lavage in a Rodent Model to Study Joint Inflammation and Posttraumatic Osteoarthritis

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Published on: September 2, 2025

Non-Invasive Compression-Induced Anterior Cruciate Ligament (ACL) Injury and In Vivo Imaging of Protease Activity in Mice

Non-Invasive Compression-Induced Anterior Cruciate Ligament (ACL) Injury and In Vivo Imaging of Protease Activity in Mice

Published on: September 29, 2023

Area of Science:

Orthopedic surgery
Sports medicine
Biomechanics

Background:

Anterior cruciate ligament (ACL) injury leads to a higher risk of reinjury, even after surgical reconstruction (ACLR).
The expected inverse relationship between muscle contraction velocity and torque production is altered post-ACLR.

Purpose of the Study:

To assess the prognostic capability of the torque-velocity relationship in predicting subsequent ACL injuries in patients recovering from primary ACLR.

Main Methods:

A descriptive laboratory study involving 579 primary unilateral ACLR patients (average 6.9 months post-surgery).
Isokinetic knee extension at 90°/s and 180°/s was performed bilaterally to calculate the torque-velocity relationship.
Reinjury outcomes were tracked for a minimum of 2 years post-surgery via phone calls and medical record reviews.

Main Results:

Approximately 14.0% of patients experienced reinjury, with similar rates across sexes and graft types.
A 1 Nm/kg increase in quadriceps torque-velocity relationship correlated with higher odds of reinjury (OR: 3.52, P=0.045).
Each additional year of age was associated with a 6% decrease in reinjury risk (OR: 0.94, P<0.01).

Conclusions:

The quadriceps torque-velocity relationship effectively predicts subsequent ACL injury post-ACLR, outperforming single-velocity assessments.
Increased patient strength may influence return-to-sport decisions, potentially increasing exposure to risk.
Clinicians should consider enhanced surveillance for strong, young patients and integrate additional risk factors for improved reinjury prediction.