Angular Kinetics - notes for biomechanics with examples of formulas and definitions PDF

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notes for biomechanics with examples of formulas and definitions ...

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Angular Kinetics: October 28, 2019 Angular Kinetics:  Kinetics is the study of causes of motion o Forces o Moments or torques  Agular Kinetics focuses on the causes of rotational motion o Focuses on moment Moments:  A force is applied directly to the COM of an object, then that object will undergo a linear acceleration proportional to and in the direction of the applied force  But if that force is applied away from objects COM that object will undergo the same linear acceleration but will also rotate about its COM  The product of an applied force and perpendicular distance from axis of rotation of the object is applied to is called a moment or moment of a force (N.m) M= F⊥d 

This moment or torque will produce a change in the objects angular velocity *** note this is similar to Newtons 2nd law

Angular Analog of Newtons Laws of Motion:  Newtons 1st Law: Law of inertia o An object at rest and a rotating object will continue to rotate with a constant angular velocity unless it experiences a net external moment  Newtons 2nd Law: Law of Acceleration o The angular acceleration of an object is directly proportional to the net moment acting on it, and is inversely proportional to its moment of inertia

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Newtons 3rd Law: Law of Action-Reaction o For every action there is an equal and opposite reaction o Ie for every action moment there is an equal and opposite reaction moment If you compare the linear and angular version of Newtons Laws

it can be seen that a moment is the angular equivalent to a force and that the moment of inertia (I) is the angular equivalent of mass *** note that the angular acceleration must be in radians ***

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Moment of Inertia:  is a measure of an object angular inertia, i.e. its tendancy to resist angular acceleration when a moment act on it o this resistance is dependent on the mass of the object and how that ass is distributed about the object’s axis of rotation o the SI units for moment of inertia is kg.m2 Moments & the Right Hand Rule

Levers:  mechanical leverage systems consist of a rigid bar-like object or lever that pivots about a fulcrum and moves or applies a force to a resistive load at some location on that lever by applying a force to another location on the lever o by their design they multiply the mechanical force that can be applied to an object

Levers & Musculoskeletal System:  the human body utilizes leverage systems to move the limbs of the body o bone are the levers o joints are the fulcrums o the body limbs and external loads the body is in contact with the resistive loads

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o the muscle provides the applied forces There are 3 arrangements of the fulcrum, applied force and load First Class Lever o Applied force and load are located on opposite sides of the fulcrum

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Second Class Lever: o The applied force and resistive load are located on the same side on the fulcrum with the resistive load in between the fulcrum and applied force

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Third Class Lever o The applied force and resistive load are located on the same side of the fulcrum with the applied force in between the fulcrum and resistive load

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Muscles have an origin on one bone and then cross one or more joints to their insertion on another bone When a muscle contracts it shortens drawing the 2 bones together o Since the line of action of the muscle is not directly thorough the joint center it creates a moment that rotates one bone about the other at the joint (ie axis of rotation) o The magnitude of that moment depends on  The force of the muscle contraction  The muscles line of action or angle of pull  The angle of pull changes as the joint angle changes throughout the motion  The location of the muscle insertion point relative to the joint center or muscle moment arm

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Recall from linear kinetics that knowledge that an object is not moving or an objects acceleration aids in the determination of unknown forces if some forces are known o The same is true for angular kinetics  Knowing that an object is not moving or an objects angular acceleration aids in the determination of the unknown’s moments if some moments are known

Mechanical Advantages:  When the distance of the aids of rotation to the applied force (moment arm) is greater than the distance from the aids of rotation to the load (load arm) the lever is said to have a mechanical advantage) o i.e the mechanical force applied to the object will be amplified to a magnitude that exceeds the force on the lever due to the object  consider a 10N objects and a 10N applied force o if the moment and load arm are both 1m

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consider a 10N objects and a 10N applied force o if the moment arm is 2m and load arm is 1m

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consider a 10N objects and a 10N applied force o if the moment arm is 1m and load arm is 2m

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thus a ratio of moment arm to the load ar that exceeds one indicates a mechanical advantage

Speed Advantage:  is the inverse of mechanical advantage

o a ratio greater than one indicates a speed advantage o although the force required to move the load is greater the loads greater distance from the axis of rotation means it will move with greater velocity...