Linear and Angular Momentum

• The notes cover fundamental concepts and definitions related to linear and angular momentum, forces, energy, and collisions, as well as their applications in biomechanics.

Linear Momentum and Inertia

• Linear momentum is the product of mass and velocity.
• Inertia is a mathematical measurement of mass.
• Inertia is the resistance to change in an object's state of motion.
• Momentum is the resistance to change in a moving object.

Angular Momentum

• Angular momentum is represented by the equation H = Imp² x W.
• H represents angular momentum.
• n is the correction factor for object shape and axis of rotation location.
• m is mass.
• p is the distance from the center of mass to the axis of rotation.
• W is angular velocity.
• Distance from the center of mass to the axis of rotation most greatly influences momentum.
• Moment of inertia is the resistance to rotation.
• A larger moment of inertia decreases rotating speed.
• A smaller moment of inertia increases rotating speed.

Propulsive vs. Braking Forces

• Propulsive forces cause a body to speed up; they are positive if the direction is positive, and negative if the direction is negative.
• Braking forces cause a body to slow down; they are positive if the direction is negative, and negative if the direction is positive.

Newton's Laws of Motion

• An object at rest or in motion stays that way unless acted upon by an outside force.
• The rate of change of momentum is proportional to the force applied and occurs in the direction of the applied force (F=ma).
• For every action force, there is an equal and opposite reaction force.

Effective Force and Mass

• Effective force is the component of a force aligned with the desired movement or displacement.
• Effective mass is the portion of a body's mass involved in a collision.
• Effective mass can be increased by increasing the mass of a segment.
• Effective mass can be increased by linking the mass of a segment/implement to the masses of other segments in the body.
• Proper positioning of segments and muscle activation is important to stiffen the extremity.

Impulse

• Impulse is the product of average force and the time the force is applied.
• Impulse is equal to the change in momentum (ΔL).
• Impulse is mass-relative impulse.
• Impulse increases primarily by increasing peak force.

Ground Reaction Force (GRF)

• Ground reaction force is the equal and opposite force that the ground applies back on a person (where all COP acts).
• During landing, kinetic energy must be absorbed by the body.
• A harder landing involves smaller displacement and higher forces over a shorter duration.
• A softer landing involves larger displacement and less force over a longer duration.
• A hard landing has a higher peak force and a shorter duration.

Rate of Force Development and Fatigue

• Rate of force development (RFD) is the rate at which force is increasing.
• Rate of force fatigue (RFF) is the rate at which force is decreasing.

Torque

• Torque is the turning effect of a force (rotational force).
• The moment arm is the perpendicular distance from the axis of rotation to the point of force application.
• Torque can be increased by increasing the length of the moment arm, increasing the magnitude of the force, or applying the force as perpendicularly as possible.

Mechanical Energy Expenditure

• Mechanical energy expenditure is work.
• Work is the process of changing (increasing or decreasing) the amount of energy in a system.
• W = F x Δp and can only occur if there is displacement
• When W is +, the energy of the system increases.
• When W is -, the energy of the system decreases, and energy is transferred to objects outside of the system.
• If work and resistance (wrap) are in opposite directions, then W is negative.
• Mechanical energy expenditure is the sum of the absolute values of W because the + and - get canceled out during a regular work example.
• MEE = Wpositive + |Wnegative|.

Definitions of Energy and Balance

• Kinetic energy is the energy a body has due to its motion.
• Gravitational potential energy is the potential energy a body has due to its position (examples include a rock held at different heights).
• Strain potential energy is the energy a body has due to deformation (example includes a rubber band).
• For static balance, the center of pressure (COP) must be within the base of support (BOS), and the COP must be under the center of gravity (COG).
• "Safety margin" of balance: the difference between the limit of sway and actual sway
• When pushed from behind, the arms rotate as quickly as possible in an anterior direction to counteract the body's COG moving backward, generating angular momentum and torque; the arms act like levers and rotational inertia generates necessary torque.

Power

• Power is the time rate of performing work.
• Power = work/time.
• Power is the ability to produce force (torque) while moving quickly.
• When a projectile is thrown into the air and comes straight back down, potential energy is greatest at the peak/apex.
• For a brief moment at the peak/apex potential energy is constant.

Elastic vs. Inelastic Collisions

• Inelastic collisions are collisions in which two objects stick together (briefly) after they collide; energy can transform into different types (sound, breaking, heat, etc.), but all energy is conserved.
• Elastic collisions are collisions in which two objects bounce off each other without deformation or loss of heat (not realistic); kinetic energy is conserved.

Coefficient of Restitution

• The coefficient of restitution is the ratio/measure of elasticity between objects (1-0).
• Closer to 1: elastic (will never see in real life) (example includes trampolines and springlines)
• Closer to 0: inelastic.
• Effective mass is the portion of a body's mass involved in a collision.
• Lining up implements improves effective mass.

Improving Effective Mass

• Mass of segment increased.
• Linking mass of segment of other segments in the region.