Transcript Biomechanics -Motion

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“How physical forces affect
human performance.”
Sir Isaac Newton
• 1642-1727
• Physicist, mathematician,
astronomer, natural philosopher,
alchemist and theologian
• “The most influential person in all
of human history.”
• Laid the basis for modern physics
•BIOMECHANICS
• Nothing more important than his
3 LAWS OF MOTION
3 Laws of Motion
2 assumptions: EQUILIBRIUM and CONSERVATION OF ENERGY
Sum of all forces
equals zero
Energy can never be
created or destroyed only
converted between forms
Law 1: INERTIA
-Every object in a state of uniform motion tends to remains in that state of
motion unless an external force is applied to it.
-ex downhill skier
Law 2: ACCELERATION
-a force applied to a body causes an acceleration of that body of a
magnitude proportional to the force, in the direction of the force.
-Ex: throwing a baseball
- F = ma
- units: Newton (N)
Law 3: REACTION
-for every action there is an equal and opposite reaction
-Ex: jumping to block a spike in volleyball
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**complete the handout on Newton’s three laws**
Types of Motion
• Linear
-movement in a direction
-force through centre of mass
-Sometimes in a straight line  sprinter running down track
-Sometimes change in direction  “juking” in football
-F = ma, v = d/t
• Rotational
-movement around an axis
-force “off-centre” of mass = rotation
-gymnast flip or skater spin
-T = F(FA), I = mr2, H = Iω, ω = ΔΘ/t
Conservation of Momentum
The total momentum of any group of objects remains the same unless outside
forces act on the objects
p = mv, m = mass
v = velocity
Units: kgm/s
Example 1 – Conservation of Linear Momentum
A 90 kg hockey player travelling with a velocity of 6 m/s
collides with an 80 kg hockey player moving at 7 m/s. What
is the resultant velocity when the two players collide?
(Since momentum is always conserved, the sum of the momentum before the collision
must equal the sum of the momentum after the collision)
m1v1 + m2v2 = mtotalvresultant
(90)(6) + (80)(-7) = (90 + 80)vresultant
-20 = 170v
-0.12 m/s = v
Rotational Motion
-remember this is motion around an axis
-rotate, turn, spin, etc
Linear Motion
Rotational Motion
Displacement
Angular
displacement ΔΘ
Angular Velocity ω
Velocity
Acceleration
Force
Angular
acceleration
Torque τ / Μ
Mass
Moment of Inertia I
Example 2 -Analyzing a figure skater spin
Part 1: How does the skater start the spin?
Outside Force
Torque = tendency of a force to rotate
an object
M = force x force arm
=Nxm
= Nm
Force = 100 N
Force arm = distance from force to fulcrum = 0.25 m
Fulcrum
Torque = M = F(FA)
M = (100N) (.25m)
= 25 Nm
So how can you manipulate this equation to increase torque?
1. Increase the amount of force
M = F(FA)
= (200)(.25)
= 50 Nm
2. Increase/Decrease force arm
M = F(FA)
M = F(FA)
= (100)(.50)
= (100)(.10m)
= 50 Nm
= 10 Nm
This explains why you grab a LONGER wrench the tougher the bolt
Example 2 -Analyzing a figure skater spin
Part 1: How does the skater start the spin?
Outside Force
Torque = tendency of a force to rotate
an object
M = force x force arm
=Nxm
= Nm
Inertia of Object
Moment of inertia = rotational inertia
I = sum of the masses x radius of gyration
= Σmr2
= kg x m x m
= kgm2
Let’s determine the moment of inertia our figure skaters would
produce doing a jump or spin.
Meghan Dwyer
Now what do we need?
Mass:
Radius of gyration (ie arm length):
I = Σmr2
Kristy Bell
Part 2 –How does the skater produce angular momentum
H = Iω
H = angular momentum
I = rotational inertia
ω = angular velocity
ω = Δθ/t
Let’s assume both girls have equal angular
velocities of 5 radians/second
What are their angular momentums?
H = Iω
H = I(5 rad/s)
H = ? Nm/s
Units = Nm/s
Part 3 –Conservation of angular momentum
Let’s play with this equation a little bit by looking at the variables during each
phase of the jump/spin
Remember: Momentum must stay the same
Phase 1: Entry
H = Iω
-arms straight out; determines momentum
Phase 2: Rotation
H = Iω
Angular velocity increases
 turn faster
-arms brought tight to body
Phase 3: Exit
H = Iω
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Increase rotational inertia
 stick out arms
-stop spin; decrease angular velocity
Example #3
A gymnast has planned to finish off her balance beam routine with a stationary
front flip as a dismount. The gymnast has a mass of 40 kg and the distance from
her hips to the tips of her fingers is 85 cm. Calculate her angular momentum if
during her flip she is able to reach an angular velocity of 3.5 radians per second?