1. “How physical forces affect human performance.”
BIOMECHANICS
-video
“How physical forces affect human performance.”

6. Sir Isaac Newton
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
Born same year Galileo died

7. 2 assumptions: EQUILIBRIUM and CONSERVATION OF ENERGY
3 Laws of Motion
2 assumptions: EQUILIBRIUM and CONSERVATION OF ENERGY
Energy can never be created or destroyed only converted between forms
Sum of all forces equals zero
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

8. **complete the handout on Newton’s three laws**
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
-video
**complete the handout on Newton’s three laws**

9. Types of Motion Conservation of Momentum Linear Rotational
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
-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 Units: kgm/s
v = velocity

10. m1v1 + m2v2 = mtotalvresultant
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) = ( )vresultant
-20 = 170v
-0.12 m/s = v

11. Rotational Motion Linear Motion Rotational Motion Displacement
-remember this is motion around an axis
-rotate, turn, spin, etc
Linear Motion
Rotational Motion
Displacement
Angular displacement ΔΘ
Velocity
Angular Velocity ω
Acceleration
Angular acceleration
Force
Torque τ / Μ
Mass
Moment of Inertia I

12. 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
= N x m
= Nm

13. Torque = M = F(FA) M = (100N) (.25m) = 25 Nm Force = 100 N
Force arm = distance from force to fulcrum = 0.25 m
Fulcrum
Torque = M = F(FA)
M = (100N) (.25m)
= 25 Nm

14. 1. Increase the amount of force
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

15. Example 2 -Analyzing a figure skater spin
Part 1: How does the skater start the spin?
Outside Force
Inertia of Object
Torque = tendency of a force to rotate an object
M = force x force arm
= N x m
= Nm
Moment of inertia = rotational inertia
I = sum of the masses x radius of gyration
= Σmr2
= kg x m x m
= kgm2

16. Let’s determine the moment of inertia our figure skaters would produce doing a jump or spin.
Meghan Dwyer Kristy Bell
Now what do we need?
Mass:
Radius of gyration (ie arm length):
I = Σmr2

17. What are their angular momentums?
Part 2 –How does the skater produce angular momentum
H = Iω
H = angular momentum
I = rotational inertia
ω = angular velocity
ω = Δθ/t
Units = Nm/s
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

18. H = Iω H = Iω H = Iω Phase 1: Entry Phase 2: Rotation Phase 3: Exit
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
Angular velocity increases  turn faster
H = Iω
-video
-arms brought tight to body
Phase 3: Exit
Increase rotational inertia  stick out arms
H = Iω
-stop spin; decrease angular velocity

19. 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?