KIN 3309 1nd Edition Lecture 18 Outline of Last Lecture I. Contact ForcesII. Free Body DiagramsIII. Effects of a Force at an Instant in TimeIV. Impulse: Force Applied over a Period of TimeV. OutlineVI. Work: Force Applied over a DistanceVII. PowerVIII. EnergyIX. Strain (Elastic Energy)X. Work-Energy TheoremXI. Conservation of EnergyXII. Energy Conversion during GaitXIII. Vectors and ScalarsXIV. Position, Displacement, DistanceXV. Velocity and AccelerationXVI. Types of AnglesXVII. Angular and Linear PositionXVIII. Angular and Linear VelocityThese 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 AccelerationXX. Centripetal (Radial) AccelerationXXI. QuizOutline of Current Lecture I. OutlineII. Linear vs. Angular MotionIII. Angular KineticsIV. TorqueV. Moment ArmVI. Manipulating TorqueVII. LeversVIII. General Lever MechanicsIX. Levers: Class 1X. Levers: Class 2XI. Levers: Class 3XII. Rotation and LeverageXIII. Eccentric (off-axis) Forces Create TorquesXIV. Force CouplesXV. Linear vs. Angular TermsXVI. Rotational Analog of Newton’s First LawXVII. Moment of InertiaXVIII. Radius of GyrationXIX. Parallel Axis of TheoremXX. Angular MomentumXXI. Conservation of Angular MomentumXXII. Rotational Analog of Newton’s Second LawXXIII. Rotational Analog of Newton’s Third LawXXIV. Newton’s Laws of MotionXXV. Example 1XXVI. Example 2XXVII. Example 3XXVIII. QuizCurrent Lecture*Final: 50 MC, 10 will be computations, 5 extra credit questionsI. Outlinea. Torque = movement of forceb. Leversc. Angular equivalents of Newton’s Lawsi. Law of inertiaii. Law of acceleration (change in momentum)iii. Law of action-reactiond. Moment of inertia (the angular equivalent of mass)e. Angular MomentumII. Linear vs. Angular Motiona. Linear Motioni. The line of application of the applied force passes through the center of mass (COM)b. Angular Motioni. 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 rotateIII. Angular Kineticsa. If the force is applied directly through the center of the object, perpendicularly tothe object (a centric force), the motion is translationalb. If the force is applied off the center, but perpendicular to the object (an eccentricforce), the object will undergo both translation and rotationIV. Torquea. The tendency of a force to rotate an object about an axis, fulcrum, or pivotb. A.K.A, moment or Moment of forcec. Torque is often referred to as rotary force and is the angular equivalent of linear forced. Torque is the product of force (f) and the perpendicular distance (d) from the force’s line of action to the axis of rotationi. A vectorii. The units of torque are newton-meters (Nm)V. Moment Arma. The perpendicular distance from the line of action of a force to the axis of rotationi. Centric force 1. Applied through axis (center) of rotation and creates no torque so causes no rotationii. Eccentric force1. Applied some distance away from axis of rotation and creates torque so causes rotationVI. Manipulating Torquea. The same size of torque can be createdi. A large force and a small moment armii. A smaller force and large moment armb. Humans tend to utilize larger moment arms regularly, because there is a limit to the amount of force humans can generate!VII. Leversa. Defined as a rigid bar that turns around an axis of rotationb. An axis is the point of rotation around which the lever movesc. The lever rotates around the axis as a result of the forced. Bones are the lever bars e. Joints are the axesf. Muscles produce the forceg. Three parts:i. Fulcrum: provides the point of rotationii. Resistance: the load you are trying to moveiii. Effort: the force you are applyingVIII. General Lever Mechanicsa. 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 torquei. Also called a moment of force, or simply a momentIX. Levers: Class 1a. Fulcrum is between effort and resistanceX. Levers: Class 2a. Resistance is between effort and fulcrumXI. Levers: Class 3a. Effort is between resistance and fulcrumb. Most of our joints are class-3 leversXII. Rotation and Leveragea. For our purposes, i. d is the perpendicular distance from the pivot to the line of action of the force1. “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 degrees2. Sin theta = 13. d = r4. Torque will be maximalb. Mechanical Advantage (MA)i. MA > 1 – larger movement of effort arm produces smaller movement in resistance armii. MA < 1 – smaller movement of effort arm produces larger movement in resistance armiii. Torque is therefore affected by the magnitude of the force and the length of the moment armc. Mechanical Advantage = 1 i. Motive arm = resistance armd. Mechanical Advantage > 1i. Effort arm > resistance armii. Force is amplifiede. Mechanical Advantage < 1 i. Effort arm < resistance armii. ROM/speed is amplifiedXIII. Eccentric (off-axis) Forces Create Torquesa. The lines of action of muscle forces do not pass through the axis of rotation of the jointb. The line of action of ground reaction forces do not always pass through the center of mass of the bodyXIV. Force Couplesa. A force couple is two parallel forces that are equal in magnitude, but act in opposite directions about an axis of rotationb. A force couple causes pure rotationXV. Linear vs. Angular Terms:a.XVI. Rotational Analog of Newton’s First Lawa. A rotating body will continue in a state of uniform angular motion unless acted upon by an external torqueb. A body’s resistance to a change in angular motion is called its moment of inertiaXVII. Moment of Inertiaa. Resistance to angular motion is dependent on massb. The more closely mass is distributed to the axis of rotation, the easier it is to rotatec. Resistance to angular motion is dependent on the distribution of massd. 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 Gyrationa. Distance from axis of rotation to a point where the body’s mass could be concentrated without altering its rotational characteristicsb. It is often expressed as a proportion of the segment length in biomechanicsc.