Applications of torques

Torques

"Angular forces" that cause angular motion.

Moment arm (r)

The distance from the axis of rotation to where the force is applied; a component of torque.

Torque (τ)

Calculated as Force applied (F) × Moment arm (r).

Linear Kinetics

Describes motion using the formula F = ma (Force = mass × linear acceleration).

Angular Kinetics

Describes motion using the formula τ = Iα (Torque = angular inertia × angular acceleration).

Angular inertia (Moment of inertia, I)

How hard it is to angularly accelerate something.

Factors determining Moment of Inertia

Depends on mass and how mass is distributed about the axis of rotation; a greater distribution of mass farther from the axis results in a greater moment of inertia.

Changing Moment of Inertia

Can be changed by shifts in posture, influencing how easily a body can rotate.

Center of Mass (CoM)/Center of Gravity (CoG)

The "balance" point where all mass is evenly distributed; approximately at the belly button in anatomical position.

Nature of Center of Gravity

A "mathematical" concept that changes with body posture and can even lie outside the body.

Base of support

The area beneath an object or person, within which the center of gravity must remain for stability; explains why stance affects stability.

Mobility

The opposite of stability, used in situations where quick movement is desired.

Torque

A rotational force dependent on the force applied and the moment arm (T = F × r).

Moment Arm

The distance from the axis of rotation to the point where an external force is applied.

Moment of Inertia

The tendency to resist changes in rotation, dependent on an object's mass and how that mass is distributed relative to the axis of rotation.

Center of Mass (CoM) / Center of Gravity (CoG)

The 'balance' point of an object where all its mass is considered to be evenly distributed. It is affected by changes in posture and mass distribution.

Small Moment of Inertia (in Gymnastics)

Achieved by gymnasts through shorter stature and adopting extremely 'tucked' postures, which allows for more rapid spinning and turning.

The 'Biles' (Gymnastics Skill)

A difficult gymnastics maneuver that requires high vertical impulse to achieve significant air time and vertical velocity, necessary to complete two rotations in a layout position despite the high moment of inertia.

Vertical Impulse

A large force applied over a period of time to create a high vertical velocity, essential for maximizing jump height in actions like the 'Biles' or high jump.

CoG Height vs. Reach Height

CoG height is determined by the vertical impulse and is the same regardless of posture. Reach height is the maximal vertical extension of the hand and depends on how far the hand is from the CoG.

Maximizing Reach Height

Achieved by increasing the distance between the hand and the center of gravity, for example, by using a one-hand reach or extending lower limbs further.

High Jump Characteristics

Successful high jumpers are typically tall (to have a naturally high CoG), run briskly (to build vertical velocity), and utilize a high vertical impulse and specific techniques to clear the bar.

Fosbury Flop

A high jump technique where the athlete arcs their back over the bar, allowing their center of gravity to pass beneath the bar, thus clearing a higher bar for the same maximum CoG height achieved.