1EXS 387 - BiomechanicsDr. MoranTuesday April 17, 2007Spring 2007Newton’s Laws“The Angular Versions”EXS 387 2• A volleyball player’s 3.7 kg arm moves at an average angular velocity of 15 rad/s during execution of a spike. If the average moment of inertia of the extending arm is 0.45 kg·m2, what is the average radius of gyration for the arm during the spike?2EXS 387 3Linear vs Angular• Comparisons between LINEAR and ANGULAR• MASS  MOMENT OF INERTIA• FORCE  TORQUE (MOMENT)• MOMENTUM  ANGULAR MOMENTUM• NEWTON’S LAWS  NEWTON’S LAW (angular version)LINEAR ANGULAREXS 387 4Newton’s First Law of MotionLINEAR• Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state of forces impressed upon it.Law of Intertia3EXS 387 5Law of Inertia – Angular Versions• What is the angular law of inertia?A rotating body will maintain a state of rest or constant rotational motion unless acted on by an external torque that changes the state.EXS 387 6Angular Law of Inertiacontinued• This is really just the principle of conservation of angular momentumIs the whole body moment of inertia CONSTANT in the human body?4EXS 387 7Angular Law of InertiacontinuedOpposite arm swings back to counteract this H and conserve angular momentumLONGITUDINAL AXISWhy would a more flexed trail leg be a good thing for a hurdler?EXS 387 8Newton’s Second Law of MotionLINEAR• The change of motion of an object is proportional to the force impressed and is made in the direction of the straight line in which the force is impressedmaF=∑∑F = net EXTERNAL forces (N)m = mass (kg)a = acceleration of object (m/s2)5EXS 387 9Newton’s 2ndLaw –Angular Versions• What is the angular law of acceleration?A net torque causes angular acceleration of a body that is:• of a magnitude proportional to the torque•• and inversely proportional to the body’s moment of inertiaEXS 387 10Angular Impulse• Angular impulse is equal to the angular momentum• So the longer a torque can be generated the more change in angular momentum can be accomplished6EXS 387 11Newton’s Third Law of MotionLINEAR• Every applied force is accompanied by a reaction force (for every action, there is an equal and opposite reaction)EXS 387 12Newton’s 3rdLaw –Angular Versions • What is the angular law of reaction?•For every angular action, • When one body exerts a torque on a second, the second body exerts a reaction torque that is equal in magnitude and opposite in direction on the first body.7EXS 387 13Angular MomentumLong Jump- To prevent the trunk/head from rotating forward (CW)rotate arm + legs CW to account for total H- Since the I’s of arms/legs are smaller than the trunk+head the ω’s of these segments must be greater than ωtrunk+headEXS 387 14END OF TEST #3MATERIAL8EXS 387 15STATIC SITUATIONCalculate Muscle Force and Joint Reaction ForceStep #1: Draw free body diagram (FBD)Step #2: Calculate and show x + y componentsStep #3: Sum forces in x-directionStep #4: Sum forces in y-directionStep #5: Sum moments about JOINT of interestStep #6: Solve for Muscle ForceStep #7: Solve for Joint Reaction Force (JRF)Step #8: Solve for direction (angle) of