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Defining the Variables

Defining the Variables. Muscle Physiology 420:289. Agenda. Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions. Introduction to Biomechanics. Biomechanics. The study of biological motion. Statics. Dynamics.

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Defining the Variables

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  1. Defining the Variables Muscle Physiology 420:289

  2. Agenda • Terminology • Systeme Internationale Base Units • Linear Derived Units • Angular Derived Units • Useful Conversions

  3. Introduction to Biomechanics Biomechanics The study of biological motion Statics Dynamics The study of forces on the body in equilibrium The study of forces on the body subject to unbalance Kinetics and Kinematics Kinetics and Kinematics Kinetics: The study of the effect of forces on the body Kinematics: The geometry of motion in reference to time and displacement Linear vs. Angular Linear vs. Angular Linear: A point moving along a line Angular: A line moving around a point

  4. Agenda • Terminology • Systeme Internationale Base Units • Linear Derived Units • Angular Derived Units • Useful Conversions

  5. SI Base Units • Base Unit: Cannot be reduced • Length: SI unit  meter (m) • Time: SI unit  second (s) • Mass: SI unit  kilogram (kg) • Distinction: Mass (kg) vs. weight (lbs.) • Mass: Quantity of matter • Weight: Effect of gravity on matter • Mass and weight on earth vs. moon?

  6. Agenda • Terminology • Systeme Internationale Base Units • Linear Derived Units • Angular Derived Units • Useful Conversions

  7. Linear SI Derived Units • Displacement: A change in position • SI unit  m • Displacement vs. distance? • Velocity: The rate of displacement • SI unit  m/s • Velocity vs. speed? • Acceleration: The rate of change in velocity • SI unit  m/s/s or m/s2

  8. Average vs. Instantaneous Velocity • Average velocity = displacement/time • Entire displacement  start to finish • Instantaneous: Velocity at any particular instant within the entire displacement • Still average velocity however time periods much smaller therefore “essentially” instantaneous

  9. Acceleration • Acceleration: Rate of change of velocity • A = vf – vi • Vector quantity • SI unit = m/s/s or m/s2 • Uniform acceleration • Very rare • Projectiles

  10. Average vs. Instantaneous Acceleration • Average acceleration = Rate of change in velocity  assumes uniform acceleration • Instantaneous: Acceleration between smaller time periods • Provides more information • Johnson vs. Lewis

  11. Average acceleration for Ben Johnson? A = (vf – vi) / t A = (10.17 m/s – 0 m/s) / 9.83 s A = (10.17 m/s) / 9.83 s A = 1.03 m/s2 Enough information? Average acceleration for Carl Lewis? A = (vf – vi) / t A = (10.14 m/s – 0 m/s) / 9.86 s A = (10.14 m/s) / 9.86 s A = 1.03 m/s2

  12. Linear SI Derived Units • Force: The product of mass and accelerationSI Unit  Newton (N)  The force that is able to accelerate 1 kg by 1 m/s2 • Rate of force development

  13. Deadlift Example Linear SI Derived Units • Work: The product of force and distance • SI Unit  Joule (J)  When 1 N of force moves through 1 m • Energy: The capacity to do work • SI Unit  J • Power: The rate of doing work (work/time) • SI Unit  Watt (W) • Note: Also calculated as F*V

  14. Agenda • Terminology • Systeme Internationale Base Units • Linear Derived Units • Angular Derived Units • Useful Conversions

  15. Angular Displacement • The change in angular position • Challenge: Difficult to describe angular displacement with linear units of measurement A B C

  16. Angular Displacement • Solution: Measure angular motion with angular units of measurement • Three interchangeable units of measurement for rotary motion: • Revolution: A complete cycle • Degree: 1/360th of a revolution • Radian: 57.3 degrees • 1 revolution = 2*p*57.3

  17. 57.3 degrees How many radians in one revolution?

  18. Angular Displacement • Angular displacement is denoted as theta (q) • q = final position – initial position • If q is not described in degrees (°), assume it is in radians

  19. Angular Velocity • The rate of angular displacement • Angular velocity is denoted as (w) • w = q / time • Unit of measurement • Rads/s or °/s • Example • A softball player who moves her arm through 3.2 radians in 0.1 s has an average w of 32 rads/s. Degrees/s? Revolutions/s?

  20. Angular Velocity • Average vs. instantaneous • Critical when analyzing sequential movements  high velocities

  21. Figure 11.16, Hamilton Sampling rate: 150 Hz Average w from a  b = 37.5 rad/s W at a = ~25 rad/s W at b = ~50 rad/s b

  22. Angular Acceleration • The rate of change in angular velocity • Angular acceleration is denoted as (a) • a = w final – w initial / time

  23. w initial = 25 rad/s Time/frame = 1/150 = 0.0067 s Number of frames from a  b = 15 Time = 15 * 0.0067 = 0.1 s a = 50 – 25 / 0.1 = 250 rad/s2 w final = 50 rad/s

  24. Angular Acceleration • Average vs instantaneous angular acceleration • Much more information

  25. Torque • Torque: The turning effect of a force • T = Fd • F = force • d = perpendicular distance between line of force and fulcrum (moment arm)

  26. F d F

  27. Torque • How can torque be modified? • Modify force • Modify moment arm • How is this accomplished in the human body?

  28. When is the moment arm length maximized in this example?

  29. Torque • T = Fd • SI Unit: Nm • Example: A muscle pulls with a force of 50 N and the moment arm is 0.02 m • Torque = (50 N)(0.02 m) = 2 Nm

  30. F = 50 N T = 50 N * 0.02 m T = 2 Nm d = 0.02 m

  31. Angular Work and Power • Work = Fd • Angular work = TDq, where • T = torque • Dq = change in angular displacement • SI unit = Nm

  32. Angular Work Example If 40.5 Nm of torque is applied by the biceps and the forearm is moved 0.79 radians, the amount of angular work performed is . . . Angular work = TDq Angular work = 40.5 Nm (0.79) Angular work = 32 Nm 0.79 rads 32 Nm of work was performed by the 40.5 Nm of torque

  33. Angular Work • Positive angular work is associated with concentric contractions • Negative angular work is associated with eccentric contractions

  34. Angular Power • Power = Fd/t or Fv • Angular power = TDq/t or Tw, where • T = torque (Nm) • Dq = change in angular displacement • T = time • w = angular velocity • SI Unit = Nm/s or Watts (W)

  35. Angular Power Example If the 32 Nm of work performed by the biceps was performed in 0.2 seconds, a net power output of . . . Angular power = TDq/t Angular power = 40.5 Nm (0.79) / 0.2 s Angular power = 32 Nm / 0.2 s Angular power = 160 Nm/s or W The angular power output of the movement was 160 W

  36. Agenda • Terminology • Systeme Internationale Base Units • Linear Derived Units • Angular Derived Units • Useful Conversions

  37. Length: 1 ft = 0.3048 m 1 m = 3.28 ft 1 inch = 2.54 cm Mass/Weight/Force: 1 N = 0.2248 lb 1 lb = 4.448 N 1 kg = 2.2 lb 1 lb = 0.454 kg 1 kg = 9.807 N Displacement: See Length Velocity: See Length Acceleration: See length Work: 1 J = 1 Nm = 0.239 cal 1 cal = 4.186 J Power: 1 W = 1 J/s 1 W = 1 Nm/s Energy: See work Angular Conversions: 1 rev = 360 degrees 1 rad = 57.3 degrees Useful Conversions http://www.wscope.com/convert.htm

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