KIN 3309 1nd Edition Lecture 19 Outline of Last 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 GyrationThese 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. 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. QuizOutline of Current Lecture I. TorqueII. LeversIII. Rotational Analog of Newton’s First LawIV. Moment of InertiaV. Angular MomentumVI. Rotational Analog of Newton’s Second LawVII. Rotational Analog of Newton’s Third LawVIII. Conservation of Angular MomentumIX. OutlineX. Centers of Mass & GravityXI. Total Body Center of MassXII. Linear vs. Angular Kinetic AnalysisXIII. Dynamic AnalysisXIV. Angular ImpulseXV. Angular WorkXVI. Angular PowerXVII. Angular EnergyXVIII. Work-Energy TheoremXIX. QuizCurrent LectureI. Torquea. Torque is often referred to as rotary force and is the angular equivalent of linear forceb. Torque is the product of force (F) and the perpendicular distance (d) from the force’s line of action to the axis of rotationi. Vector!ii. The units of torque are newton-meters (Nm)II. Leversa. Three parts:i. Fulcrum: provides the point of rotationii. Resistance: the load you are trying to moveiii. Effort: the force you are applyingIII. 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 inertiaIV. Moment of Inertiaa. The inertial property for rotating bodiesb. Represents resistance to angular accelerationc. Based on both mass and the distance the mass is distributed from the axis of rotationV. Angular Momentuma. The quality of angular motion that a body possessb. H = I x omegai. Angular momentum is represented by Hii. Angular momentum has units of kg x m2 / siii. H is the rotational equivalent of linear momentum (p = mv)VI. Rotational Analog of Newton’s Second Lawa. The rate of change of angular momentum of a body is proportional to the torque causing it and the change takes place in the direction in which the torque actsVII. Rotational Analog of Newton’s Third Lawa. For every torque that is exerted by one body on another there is an equal and opposite torque exerted by the second body on the firstVIII. Conservation of Angular Momentuma. When gravity is the only external force acting on an object, the angular momentum remains constant i. This is because the gravitational force acts through the center of mass of an object (point of rotation) and therefore does not produce a torqueb. This allows divers and gymnasts to manipulate their angular velocities by changing their moments of inertiac. When angular momentum is conserved, there is a tradeoff between moment of inertia and angular velocityi. Tuck position = small I, large omegaii. Extended position = large I, small omegaIX. Outlinea. Torquesi. Static and dynamic analysisb. Angular impulsec. Angular workd. Angular powere. Angular energyf. Work-Energy TheoremX. Centers of Mass & Gravitya. The center of mass (CM) is the theoretical point about which the body mass is evenly distributedb. CM is used interchangeably with more restrictive center of gravity (CG), which is the theoretical point which the sum of all torques due to gravity equal zeroXI. Total Body Center of Massa. You can move your center of mass by redistributing your weight (i.e., changing your body posture)XII. Linear vs. Angular Kinetic Analysisa. Static Analysisi. Linear1. Systems at rest or constant velocityii. Angular1. Applies to systems at rest or at constant b. Dynamic Analysisi. Linear1. Systems in motion (accelerating of decelerating)ii. Angular1. Applies to systems in motion undergoing angular accelerationXIII. Dynamic Analysisa. If angular acceleration is significant, then a dynamic analysis is requiredb. Biomechanists usually evaluate each segment from a distal end and work systematically up each segment linki. This is known as an inverse dynamic analysisXIV. Angular Impulsea. Torque applied over a period of timei. Impulse is vector quantity, the direction is the same as the direction of the forceii. Symbolized as Liii. Units = kgm2 / sb. Impulse = change in momentumXV. Angular Worka. Torque applied over an angular displacementi. Work is a scalar quantityb. Positive work (concentric muscle actions)c. Negative work (eccentric muscle actionsXVI. Angular Powera. The rate of change in angular worki. Angular power is the rate of change in angular workii. Units of power are watts (J/s)iii. Power is a scalar quantityXVII. Angular Energya. The capacity to do work due to rotational motionXVIII. Work-Energy Theorema. Work angular = change in rotational energyb. This again assumes that no work is done to deform the object (i.e., no strain energy is storedXIX. Quiza. The moment arm of the biceps brachii muscle about the elbow joint is largest when the angle at the elbow joint is approximately _____i. 180 degreesii. 150 degreesiii. 120 degreesiv. 90 degreesb. For a body to be in static equilibrium, ____i. All forces acting on the body must sum to zeroii. All torques acting on the body must sum to zeroiii. The body must be stationaryiv. All of the abovec. Angular impulse is the product ofi. Force and the time that force is applied (this is linear impulse)ii. Torque and the time that torque is applied T x delta Tiii. Angular inertia and angular momentumiv. Mass and angular velocityv. Force and