defining the variables

Defining the Variables

Muscle Physiology420:289

Agenda

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

Introduction to BiomechanicsBiomechani

csStatics 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 bodyKinematics: The geometry of motion in reference to time and displacement

Linear: A point moving along a lineAngular: 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) / tA = (10.17 m/s – 0 m/s) / 9.83 sA = (10.17 m/s) / 9.83 sA = 1.03 m/s2

v BJ (m/s) v CL (m/s)0 0

5.38 5.326.97 6.767.89 7.738.58 8.399.01 8.919.40 9.309.71 9.609.86 9.85

10.02 10.0110.17 10.14

Average acceleration for Carl Lewis?A = (vf – vi) / tA = (10.14 m/s – 0 m/s) / 9.86 sA = (10.14 m/s) / 9.86 sA = 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 HzAverage from a b = 37.5 rad/sW at a = ~25 rad/sW 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 sNumber of frames from a b = 15Time = 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/tAngular power = 40.5 Nm (0.79) / 0.2 sAngular power = 32 Nm / 0.2 sAngular power = 160 Nm/s or WThe 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