“How physical forces affect human performance.”

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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

**complete the handout on Newton’s three laws**

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Types of Motion• 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 MomentumThe 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

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

Velocity Angular Velocity ω

Acceleration Angular acceleration

Force 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

= N x m

= Nm

Fulcrum

Force = 100 N

Force arm = distance from force to fulcrum = 0.25 m

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

= N x m

= 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 Kristy Bell

Now what do we need?

Mass:

Radius of gyration (ie arm length):

I = Σmr2

Part 2 –How does the skater produce angular momentum

H = IωH = angular momentum

I = rotational inertia

ω = angular velocity

ω = Δθ/t

Units = Nm/sLet’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

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

Phase 1: Entry

Remember: Momentum must stay the same

H = Iω-arms straight out; determines momentum

Phase 2: Rotation

H = Iω-arms brought tight to body

Phase 3: Exit

Angular velocity increases turn faster

-stop spin; decrease angular velocityH = Iω

Increase rotational inertia stick out arms

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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?