KIN 3309 1nd Edition Lecture 18 Outline of Last Lecture I Contact Forces II Free Body Diagrams III Effects of a Force at an Instant in Time IV Impulse Force Applied over a Period of Time V Outline VI Work Force Applied over a Distance VII Power VIII Energy IX Strain Elastic Energy X Work Energy Theorem XI Conservation of Energy XII Energy Conversion during Gait XIII Vectors and Scalars XIV Position Displacement Distance XV Velocity and Acceleration XVI Types of Angles XVII Angular and Linear Position XVIII Angular and Linear Velocity These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute XIX Tangential Acceleration XX Centripetal Radial Acceleration XXI Quiz Outline of Current Lecture I Outline II Linear vs Angular Motion III Angular Kinetics IV Torque V Moment Arm VI Manipulating Torque VII Levers VIII General Lever Mechanics IX Levers Class 1 X Levers Class 2 XI Levers Class 3 XII Rotation and Leverage XIII Eccentric off axis Forces Create Torques XIV Force Couples XV Linear vs Angular Terms XVI Rotational Analog of Newton s First Law XVII Moment of Inertia XVIII Radius of Gyration XIX Parallel Axis of Theorem XX Angular Momentum XXI Conservation of Angular Momentum XXII Rotational Analog of Newton s Second Law XXIII Rotational Analog of Newton s Third Law XXIV Newton s Laws of Motion XXV Example 1 XXVI Example 2 XXVII Example 3 XXVIII Quiz Current Lecture Final 50 MC 10 will be computations 5 extra credit questions I Outline a Torque movement of force b Levers c Angular equivalents of Newton s Laws i Law of inertia ii Law of acceleration change in momentum iii Law of action reaction d Moment of inertia the angular equivalent of mass e Angular Momentum II Linear vs Angular Motion a Linear Motion i The line of application of the applied force passes through the center of mass COM b Angular Motion i The line of application of the applied force does not pass through the center of mass or axis of rotation of the object then the object will rotate III Angular Kinetics a If the force is applied directly through the center of the object perpendicularly to the object a centric force the motion is translational b If the force is applied off the center but perpendicular to the object an eccentric force the object will undergo both translation and rotation IV Torque a The tendency of a force to rotate an object about an axis fulcrum or pivot b A K A moment or Moment of force c Torque is often referred to as rotary force and is the angular equivalent of linear force d Torque is the product of force f and the perpendicular distance d from the force s line of action to the axis of rotation i A vector ii The units of torque are newton meters Nm V Moment Arm a The perpendicular distance from the line of action of a force to the axis of rotation i Centric force 1 Applied through axis center of rotation and creates no torque so causes no rotation ii Eccentric force 1 Applied some distance away from axis of rotation and creates torque so causes rotation VI Manipulating Torque a The same size of torque can be created i A large force and a small moment arm ii A smaller force and large moment arm b Humans tend to utilize larger moment arms regularly because there is a limit to the amount of force humans can generate VII Levers a b c d e f g Defined as a rigid bar that turns around an axis of rotation An axis is the point of rotation around which the lever moves The lever rotates around the axis as a result of the force Bones are the lever bars Joints are the axes Muscles produce the force Three parts i Fulcrum provides the point of rotation ii Resistance the load you are trying to move iii Effort the force you are applying VIII General Lever Mechanics a In order for a force to cause a rotation it must act at some distance from the point of rotation fulcrum b Such a force generates a torque i Also called a moment of force or simply a moment IX Levers Class 1 a Fulcrum is between effort and resistance X Levers Class 2 a Resistance is between effort and fulcrum XI Levers Class 3 a Effort is between resistance and fulcrum b Most of our joints are class 3 levers XII Rotation and Leverage a For our purposes i d is the perpendicular distance from the pivot to the line of action of the force 1 effort moment arm 2 muscle moment arm ii Note that when the line of action of the force is perpendicular to the beam 1 Theta is 90 degrees 2 Sin theta 1 3 d r 4 Torque will be maximal b Mechanical Advantage MA i MA 1 larger movement of effort arm produces smaller movement in resistance arm ii MA 1 smaller movement of effort arm produces larger movement in resistance arm iii Torque is therefore affected by the magnitude of the force and the length of the moment arm c Mechanical Advantage 1 i Motive arm resistance arm d Mechanical Advantage 1 i Effort arm resistance arm ii Force is amplified e Mechanical Advantage 1 i Effort arm resistance arm ii ROM speed is amplified XIII Eccentric off axis Forces Create Torques a The lines of action of muscle forces do not pass through the axis of rotation of the joint b The line of action of ground reaction forces do not always pass through the center of mass of the body XIV Force Couples a A force couple is two parallel forces that are equal in magnitude but act in opposite directions about an axis of rotation b A force couple causes pure rotation XV Linear vs Angular Terms a XVI Rotational Analog of Newton s First Law a A rotating body will continue in a state of uniform angular motion unless acted upon by an external torque b A body s resistance to a change in angular motion is called its moment of inertia XVII Moment of Inertia a Resistance to angular motion is dependent on mass b The more closely mass is distributed to the axis of rotation the easier it is to rotate c Resistance to angular motion is dependent on the distribution of mass d If the mass of the object are concentrated at a single point the center of mass how far from the axis would it have to be located to have the same moment of inertia XVIII Radius of Gyration a Distance from axis of rotation to a point where the body s mass could be concentrated without altering its rotational characteristics b It is often expressed as a proportion of the segment length in biomechanics c When knee flexion is increased during running the moment of inertia of the lower extremity about the hip is decreased XIX Parallel Axis Theorem a