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
The study of forces on the body in equilibrium
Kinetics and Kinematics
Dynamics
The study of forces on the body subject to unbalance
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
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
unit  m
 Displacement vs. distance?
 SI

Velocity: The rate of displacement
unit  m/s
 Velocity vs. speed?
 SI

Acceleration: The rate of change in velocity
 SI
unit  m/s/s or m/s2
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. BJ
Vinst. CL
10
1.86
1.88
5.38
5.32
10 20
1.01
1.08
9.90
9.26
20 30
0.93
0.92
10.75
10.87
30 40
0.86
0.89
11.63
11.24
40 50
0.89
0.84
11.24
11.90
50 60
0.83
0.84
12.05
11.90
60 70
0.83
0.84
12.05
11.90
70 80
0.90
0.83
11.11
12.05
80 90
0.87
0.87
11.49
11.49
90 100
0.85
0.87
11.76
11.49
0
Instantaneous Velocity Figure - Johnson vs. Lewis (1988 Summer Olympics,
Seoul Korea)
13.00
12.00
Velocity (m/s)
11.00
10.00
Johnson
9.00
Lew is
8.00
7.00
6.00
5.00
0 10
10 20
20 30
30 40
40 50
50 60
Meters (m)
60 70
70 80
80 90
90 100
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
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
v BJ (m/s) v CL (m/s)
0
0
5.38
5.32
6.97
6.76
7.89
7.73
8.58
8.39
9.01
8.91
9.40
9.30
9.71
9.60
9.86
9.85
10.02
10.01
10.17
10.14
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
(m)
Splits BJ (s)
Splits CL (s)
Vinst. BJ
Vinst. CL
10
1.86
1.88
5.38
5.32
2.89
2.83
10 20
1.01
1.08
9.90
9.26
4.48
3.65
20 30
0.93
0.92
10.75
10.87
0.92
1.75
30 40
0.86
0.89
11.63
11.24
1.02
0.41
40 50
0.89
0.84
11.24
11.90
-0.44
0.80
50 60
0.83
0.84
12.05
11.90
0.98
0.00
60 70
0.83
0.84
12.05
11.90
0.00
0.00
70 80
0.90
0.83
11.11
12.05
-1.04
0.17
80 90
0.87
0.87
11.49
11.49
0.44
-0.64
0
a BJ (m/s2)
a CL (m/s2)
Instantaneous Acceleration Figure - Johnson vs. Lewis (1988 Summer
Olympics, Seoul Korea)
5.00
Velocity (m/s/s)
4.00
3.00
2.00
Johnson
Lew is
1.00
0.00
0 10
10 20
20 30
30 40
40 50
50 60
-1.00
-2.00
Meters (m)
60 70
70 80
80 90
90 100
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

Linear SI Derived Units

Deadlift
Example
Work: The product of force and distance
Unit  Joule (J)  When 1 N of force moves
through 1 m
 SI

Energy: The capacity to do work
 SI

Unit  J
Power: The rate of doing work (work/time)
Unit  Watt (W)
 Note: Also calculated as F*V
 SI
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
A
B
C
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
57.3 degrees
How many radians in
one revolution?
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

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?
Angular Velocity
Average vs. instantaneous
 Critical when analyzing sequential
movements  high velocities

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
Angular Acceleration
The rate of change in angular velocity
 Angular acceleration is denoted as (a)
 a = w final – w initial / time

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
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
T = 50 N * 0.02 m
T = 2 Nm
d = 0.02 m
Angular Work and Power
Work = Fd
 Angular work = TDq, where

T
= torque
 Dq = 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 = TDq
0.79 rads
Angular work = 40.5 Nm (0.79)
Angular work = 32 Nm
32 Nm of work was performed by
the 40.5 Nm of torque
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 = 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)
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
Agenda
Terminology
 Systeme Internationale Base Units
 Linear Derived Units
 Angular Derived Units
 Useful Conversions

Useful Conversions

Length:




Displacement:



Power:



1 W = 1 J/s
1 W = 1 Nm/s
Energy:


1 J = 1 Nm = 0.239 cal
1 cal = 4.186 J
See work
Angular Conversions:


1 rev = 360 degrees
1 rad = 57.3 degrees
See Length
Velocity:


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
Work:


Mass/Weight/Force:






1 ft = 0.3048 m
1 m = 3.28 ft
1 inch = 2.54 cm

See Length
Acceleration:

See length
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