Biomechanics Linear motion This is motion in a straight line Definitions: Speed: distance moved in a given time Velocity: displacement in a given time Acceleration: change in velocity over a given time Units : Speed and velocity metres per second Acceleration: metres per second per second

Force and Newton’s Laws Sports involve the application of forces A force is something that will change the state of motion of whatever it is applied to Force is measured in Newton’s

Newton’s First Law “An object at rest will remain at rest or if is moving with a constant velocity will continue to move with a constant velocity unless it is acted on by an external force” Sometimes called the law of inertia This is the reluctance of an object to start or stop moving It is related to mass Heavy objects have more inertia

Newton’s Second Law “The acceleration of a body is proportional to the force causing it, and the acceleration takes place in the direction in which that force acts” This is usually expressed as f = ma F = force M = mass A = acceleration

Questions 1.A sprinter has a mass of 74kg. What force is required to give the athlete an acceleration of 4.6m/s/s? 2.A footballer kicks a football of mass 0.7 kg with a force of 14n. Calculate the initial acceleration of the ball.

Newton’s Second Law - extended version F = ma (1) Acceleration = change in velocity Time taken to change This could be expressed as: final velocity - initial velocity Time taken to change This can be expressed in symbols as: A = V – U where A = acceleration, V = final velocity, T U= initial velocity, T = time Substitute this for a in equation (1) F = m ( v-u ) or f = mv - mu T t

Impulse and momentum Newton’s second law brings in two other concepts Momentum This is the amount of motion an object has It is the product of its mass and velocity Momentum = mass x velocity Impulse This is the product of the force and the time a force is in contact with an object Impulse = force x time

Going back to Newton’s second law (extended version) F = mv - mu T If this is rearranged we get: Ft = mv - mu Ft = impulse Mv – mu = momentum change So impulse = momentum change

Newton’s Third Law “When one object exerts a force on a second object, there is a force equal in magnitude but opposite in direction exerted by the second object on the first” More simply To every action there is an equal and opposite reaction Sprinter pushes against blocks Blocks push back against sprinter

Impulse and force/time graphs The concept of impulse can be represented by a force – time graph force time a b The diagram represents a racket hitting a ball. Point a is where the strings first make contact with the ball, point b is where the ball leaves the racket

Force –time graphs showing the foot contact in a sprint race Positive impulse bigger than negative Therefore runner is accelerating This happens at the beginning of the race f+ t - Positive and negative impulses equal Runner is neither gaining or losing speed Constant velocity This happens in the middle of a race f t

f+ t - Bigger negative impulse than positive Therefore runner is slowing down This happens at the end of a race Physiological reason - PC stores running out f+ t - No negative impulse Therefore the runner hasn’t touched the track yet They are pushing off from the starting blocks Two peaks show that impulse is being exerted by both legs at slightly different times

Projectile motion When an object such as a shot is thrown, the path the flight of the shot takes is known as a PARABOLIC CURVE. When the shot is thrown, both vertical and horizontal forces are acting on the ball since it is moving both upwards(and downwards), and across. These forces can be represented by force arrows (vectors) to show the different magnitudes of the horizontal and vertical components

A B

Angular motion/movement Angular motion/movement describes bodies that are in full or part rotation about an axis. Newton’s first law of angular motion A rotating body will continue to turn about its axis of rotation with constant angular momentum unless an external couple or eccentric force acts upon it. This law is also known as the conservation of angular momentum

So what is angular momentum? Angular momentum = moment of inertia x angular velocity The moment of inertia (M.I) is the resistance to rotation or angular motion. When already rotating it is the resistance of that body to change its state of rotation. Angular velocity is the rate of movement in rotation. Quite simply it is how fast it is spinning!

So how does angular momentum work? 1.Sit in a chair that rotates. 2.Get a partner to start spinning you round. 3.Bring in your arms and legs as close to yourself as possible. 4.Now stick your arms and legs out as far as you can. What happened during these two stages?

The theory behind it all…….. M.I is determined by its mass and the distribution of its mass around its axis of rotation. The further away the mass (your legs and arms) are from the axis of rotation, the greater its moment of inertia and more force will be required to make it spin or stop it spinning. The closer the mass (your arms and legs) are to the axis of rotation the smaller its moment of inertia will be and less force will be required to make it spin or stop spinning. Remembering that angular momentum must be constant……….. when the MI is high the angular velocity must be? when the MI is low the angular velocity must be?

Examples of angular momentum in sport A spin in ice skating Explain what is happening in (a) and (b) in relation to angular momentum, moment of inertia and angular velocity (a) (b)

Examples of angular momentum in sport A high board dive Explain what is happening in (a) and (b) in relation to angular momentum, moment of inertia and angular velocity (a) (b)

Question: Explain why it is easier to perform a tuck somersault compared to an open somersault?

Answer In a layout the mass is distributed away from axis So moment of inertia is larger So more force is needed to start rotation Rotation as a result will be slower As AM = MI x AV AM stays constant since only gravity is acting on the body In a tuck the mass is closer to axis So moment of inertia is smaller So less force is needed to start rotation Rotation as a result will be quicker Making performance easier

Past exam questions