“How physical forces affect human performance.” BIOMECHANICS -video “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 Born same year Galileo died

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

**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**

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

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) = (90 + 80)vresultant -20 = 170v -0.12 m/s = v

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

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

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

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

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

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

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

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

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?