The Biomechanical Model for Minimum Movement Time during Running Walking and Road Cycling 06: The Angular Impulse-Momentum Principle

The fifth fundamental Biomechanical principle included in this model is the Angular Impulse-Momentum Principle. This principle states that an increase in angular velocity of a body segment is caused by an increase in the joint torque (i.e., the turning effect caused by a muscle force), and/or an increase in the application time of the joint torque (i.e., the amount of time the joint torque is applied at the joint) and/or a decrease in the body component’s angular inertia (i.e., the resistance of the body component being moved to the angular motion).

The equation for the Angular Impulse – Momentum Principle is given here

Here is a graphical representation of the Angular Impulse – Momentum Principle.

Click on "read more" to view my description of the application of the Angular Impulse-Momentum Principle to real-world running.


In Post 05 for the Biomechanical Model for Minimum Movement Time during Running Walking and Road Cycling, I ended the post by stating I would discuss how to increase joint angular velocity in an upcoming post.  Well, this is the post.

There are three factors that determine the magnitude of a joint's angular velocity: the magnitude of the joint torque, the application time of the joint torque; and magnitude of the angular inertia of the body component resisting the joint torque.

If we increase the magnitude of the joint torque and/or the magnitude of the application time of the joint torque, then joint angular velocity will increase as long as the magnitude of the angular inertia of the body component resisting the joint torque remains constant.

Alternatively, if we decrease the magnitude of the angular inertia of the body component resisting the joint torque, then joint angular velocity will increase as long as magnitude of the joint torque and the magnitude of the application time of the joint torque remain constant.

Increasing the magnitude of the joint torque and reducing the magnitude of the angular inertia of the body component resisting the joint torque will be discussed in upcoming posts.  Increasing the application time of the joint torque will be discussed here.


Increasing application time of each joint torque is accomplished by understanding that every joint rotation has two phases: the preparation phase and the execution phase. During the preparation phase, the joint rotates in the opposite direction from the desired rotation. For example, one of the required joint rotations for running is hip extension. During the preparation phase, hip flexion must be performed. Once the preparation phase has been performed; it is immediately followed by the execution phase. During the execution phase, hip extension would be performed. Therefore, to increase the application time of the hip extension torque, you must perform two actions; optimally flex the hip during the preparation phase and maximally extend the hip during the execution phase.

During running, the preparation phase begins when the foot collides with the ground and ends when the foot is under the center of mass of the body. The execution phase begins when the preparation phase ends and ends when the foot leaves the ground.

The optimization of hip flexion during the preparation phase depends on the environment in which the activity is being performed and on the muscle properties of the individual who is running. If the activity is performed in a closed environment (i.e., an environment where the relevant stimuli in the environment for making a decision to move are static (i.e., not changing), then the optimal amount of hip flexion would be 120% of the muscle resting lengths.  Running on a track with no other runners would be an example of a closed environment.


If on the other hand, if the activity is performed in an open environment (i.e., an environment where the relevant stimuli in the environment for making a decision to move are dynamic (i.e., changing), then the optimal amount of hip flexion would be determined by a cognitive evaluation of these relevant stimuli. Cross country running would be an example of an open environment.

Muscle fiber type (slow-twitch fibers versus fast-twitch fibers) will also influence the optimal amount of hip flexion, knee flexion, and ankle dorsiflexion during the preparation phase. Fast-twitch fibers generate maximum muscle force is a shorter amount of time than slow-twitch fibers. Therefore, an individual with a greater amount of fast twitch fibers in the hip extensor muscles would need a smaller optimal amount of hip flexion during the preparation phase.