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

Agenda Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions

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?

Agenda Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions

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/s 2

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

(m)Splits BJ (s)Splits CL (s)Vinst. BJVinst. CL

Acceleration Acceleration: Rate of change of velocity  A = v f – v i Vector quantity SI unit = m/s/s or m/s 2 Uniform acceleration  Very rare  Projectiles

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

Average acceleration for Ben Johnson? A = (v f – v i ) / t A = (10.17 m/s – 0 m/s) / 9.83 s A = (10.17 m/s) / 9.83 s A = 1.03 m/s 2 v BJ (m/s)v CL (m/s) Average acceleration for Carl Lewis? A = (v f – v i ) / t A = (10.14 m/s – 0 m/s) / 9.86 s A = (10.14 m/s) / 9.86 s A = 1.03 m/s 2 Enough information?

(m) Splits BJ (s)Splits CL (s) Vinst. BJVinst. CL a BJ (m/s2)a CL (m/s2)

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/s 2 Rate of force development

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 Deadlift Example

Agenda Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions

Angular Displacement The change in angular position Challenge: Difficult to describe angular displacement with linear units of measurement ABC

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

57.3 degrees How many radians in one revolution?

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

Angular Velocity The rate of angular displacement Angular velocity is denoted as (  )  =  / 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  of 32 rads/s. Degrees/s? Revolutions/s?

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

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

Angular Acceleration The rate of change in angular velocity Angular acceleration is denoted as (  )  =  final –  initial / time

 initial = 25 rad/s  final = 50 rad/s Time/frame = 1/150 = s Number of frames from a  b = 15 Time = 15 * = 0.1 s  = 50 – 25 / 0.1 = 250 rad/s 2

Angular Acceleration Average vs instantaneous angular acceleration Much more information

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

F d F

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

When is the moment arm length maximized in this example?

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

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

Angular Work and Power Work = Fd Angular work = T , where  T = torque   = change in angular displacement SI unit = Nm

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 = T  Angular work = 40.5 Nm (0.79) Angular work = 32 Nm 32 Nm of work was performed by the 40.5 Nm of torque 0.79 rads

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

Angular Power Power = Fd/t or Fv Angular power = T  /t or T , where  T = torque (Nm)   = change in angular displacement  T = time   = angular velocity SI Unit = Nm/s or Watts (W)

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 = T  /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

Agenda Terminology Systeme Internationale Base Units Linear Derived Units Angular Derived Units Useful Conversions

Length:  1 ft = m  1 m = 3.28 ft  1 inch = 2.54 cm Mass/Weight/Force:  1 N = lb  1 lb = N  1 kg = 2.2 lb  1 lb = kg  1 kg = N Displacement:  See Length Velocity:  See Length Acceleration:  See length Work:  1 J = 1 Nm = cal  1 cal = 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