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
Statics Dynamics
Kinetics and Kinematics
Kinetics and Kinematics
Linear vs. Angular Linear vs. Angular
The study of biological motion
The study of forces on the body in equilibrium
The 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 matterWeight: Effect of gravity on matterMass 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/s2
Average vs. Instantaneous Velocity Average velocity = displacement/time
Entire displacement start to finish Instantaneous: Velocity at any particular
instant within the entire displacementStill average velocity however time periods
much smaller therefore “essentially” instantaneous
(m) Splits BJ (s) Splits CL (s) Vinst. BJ Vinst. CL
0 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
Instantaneous Velocity Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100
Meters (m)
Velo
city
(m/s
)
Johnson
Lew is
Acceleration
Acceleration: Rate of change of velocityA = vf – vi
Vector quantity SI unit = m/s/s or m/s2
Uniform accelerationVery rareProjectiles
Average vs. Instantaneous Acceleration Average acceleration = Rate of change in
velocity assumes uniform acceleration Instantaneous: Acceleration between
smaller time periodsProvides more informationJohnson vs. Lewis
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
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 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
Enough information?
(m) Splits BJ (s) Splits CL (s) Vinst. BJ Vinst. CL a BJ (m/s2) a CL (m/s2)
0 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
90 100 0.85 0.87 11.76 11.49 0.32 0.00
Instantaneous Acceleration Figure - Johnson vs. Lewis (1988 Summer Olympics, Seoul Korea)
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100
Meters (m)
Velo
city
(m/s
/s)
Johnson
Lew is
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
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
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 cycleDegree: 1/360th of a revolutionRadian: 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 = 0.0067 s
Number of frames from a b = 15
Time = 15 * 0.0067 = 0.1 s
= 50 – 25 / 0.1 = 250 rad/s2
Angular Acceleration
Average vs instantaneous angular acceleration
Much more information
Torque
Torque: The turning effect of a force T = Fd
F = forced = 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 mT = 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 displacementT = 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
Useful Conversions
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
http://www.wscope.com/convert.htm