1.3b linear + angular motion fluids and projectiles

• linear motion

  movement of a body in a straight or curved line, where all parts move the same distance, in the same direction over the same time

  linear motion results from a direct force being applied to a body, where the force is applied directly to the centre of a body's mass
• linear motion descriptors

  1. distance
  2. displacement
  3. speed
  4. velocity
  5. acceleration / deceleration
• distance

  the total length of the path covered from start to finish (or position A to B). measured in metres (m)
• displacement

  the shortest straight-line route from start to finish (or position A to B). displacement is measured in metres (m)
• speed

  speed is the rate of change in distance

  speed = distance / time taken

  speed is measured in metres per second (m/s), distance in metres (m) and time taken in seconds (s)
• velocity

  velocity is the rate of change in displacement

  velocity = displacement / time taken

  velocity is measured in metres per second (m/s), displacement is measured in metres (m) and time taken in seconds (s)
• acceleration / deceleration

  the rate of change in velocity

  acceleration = (final velocity - initial velocity) / time taken

  acceleration is measured in metres per second per second (m/s/s), change in velocity measured in metres per second (m/s) and time taken in seconds (s)

  deceleration occurs when the rate of change in velocity is negative or there is a decrease in velocity over time
• distance / time graphs

  shows the distance a body travels over a period of time. the gradient of the curve indicates the speed of the body at a particular instant and will show whether the body is at rest, travelling with constant speed, accelerating or decelerating. using the distance / time curve, the speed can be calculated at any given point using

  speed = distance / time
• speed / time graphs

  shows the speed of a body over a period of time. the gradient of the curve indicates the acceleration of the body at a particular instant and will show whether the body is at rest, travelling with constant speed, accelerating or decelerating. using the speed / time curve, distance travelled can be measured as the area under the speed / time curve is equal to the distance travelled by a body
• velocity / time graphs

  shows the velocity of a body over a period of time. the gradient of the curve indicates the acceleration of the body at a particular instant and will show whether the body is at rest, travelling with uniform velocity, accelerating or decelerating. using the velocity time curve, acceleration can be calculated at any given point using the formula

  acceleration = (final velocity - initial velocity) / time taken
• angular motion

  movement of a body or part of a body in a circular path about an axis of rotation

  angular motion results from an eccentric force being applied to a body where the force is applied outside the centre of mass. an eccentric force is also known as a torque- a turning or rotational force
• principal axis of rotation

  an imaginary line that passes through the centre of mass about which a body rotates: longitudinal, transverse and frontal axis
• • longitudinal axis runs from head to toe through the centre of mass. a body rotating around the longitudinal axis will be performing actions such as a flat spin on the ice or a full turn in trampolining
  • transverse axis runs from left to right through the centre of mass. a body rotating through the transverse axis will be performing actions such as a somersault
  • frontal axis runs from front to back through the centre of mass. a body rotating around the frontal axis will be performing actions such as cartwheels
• angular motion descriptors

  1. angular velocity
  2. moment of inertia
  3. angular momentum
• angular motion is measured in radians (rad), which is a unit of measurement of the angle through which a body rotates. 1 radian = 57.3 degrees
• angular velocity

  the rate of change in angular displacement, or rate of rotation

  angular velocity = angular displacement / time taken

  angular velocity is measured in radians per second (rad/s), angular displacement is measured in radians (rad) and time taken in seconds (s)
• moment of inertia

  the resistance of a body to change its state if angular motion or rotation. a resting body will not want to start rotating an axis ad a rotating body will not want to change its angular motion or momentum; it will resist increasing or decreasing the rate of spin. moment of inertia is the angular or rotational equivalent of inertia

  moment of inertia = Σ mass x distribution of mass from the axis of rotation2

  moment of inertia is measured in kilogram metres2 (kgm2), mass in kilograms (kg) and distribution of mass from the axis of rotation in metres2 (m2)
• how mass affects moment of inertia

  the greater the mass of a body, the greater the moment of inertia. sports with a high degree of rotation or technical requirement for complex twists or spins, such as high board diving and gymnastics, are performed with athletes with a low mass

  • the low mass decreases moment of inertia and the resistance to change state of rotation, so athlete can start rotation, change the rate of rotation and stop rotation with relative ease
• how distribution of mass from the axis of rotation affects moment of inertia

  the further the mass moves from the axis of rotation, the greater the moment of inertia. movements where the mass is tucked in around the axis of rotation such as a front tucked somersault, lower the moment of inertia

  • the close "tucked" mass distribution from the axis of rotation decreases the moment of inertia and the resistance to change state of rotation. when performing a front tucked somersault the body will face less resistance to rotation and therefore rotate more quickly compared with a straight somersault
• considering running technique, both legs are the same mass, so should have the same moment of inertia, but:

  • recovery legs mass is distributed close to axis of rotation at the hip, and so moment of inertia is low- resistance to rotation is low and the leg moves back to the ground quickly
  • drive legs mass is distributed far from axis of rotation at the hip and so moment of inertia is high- resistance to rotation is high and the leg moves slowly

  sprint training involves drills to encourage maximum flexion at knee joint, keeping recovery leg close to hip joint, rotating it quickly to the ground
• moment of inertia has a direct effect on angular velocity:

  • if moment of inertia is high, resistance to rotation is also high, therefore angular velocity is low: the rate of spin is low
  • if moment of inertia is low, resistance to rotation is also low, therefore angular velocity is high: the rate of spin is fast
• moment of inertia in an action can be manipulated to perform complex movement patters e.g., an ice skater performing a static spin on the ice will manipulate their body position to maximise the spin. spinning around the longitudinal axis with body mass tucked into their body (bringing arms and legs closer to the body midline), the skater reduces their moment of inertia, increasing angular velocity, and rotate quickly. moving their limbs away from the axis of rotation, increases their moment of inertia, reducing angular velocity and decreasing their rate of spin
• angular momentum

  the quantity of angular motion possessed by a body. it is the rotational equivalent of momentum

  angular momentum = moment of inertia x angular velocity

  angular momentum is measured in kilogram metres squared radians per second (kgm2rad/s), moment of inertia in kilogram metres squared (kgm2) and angular velocity in radians per second (rad/s)
• to start rotating around an axis, angular momentum must be generated. in the preparation or take off phase of a rotational movement pattern, an eccentric force or torque must be applied e.g., a high board diver must jump away from the diving board and create rotation. they lean away from the board at take off so the reaction force generated from the diving board passes outside their centre of mass (lean back to create a spinning effect), creating an eccentric force and generates angular momentum. the greater the size of an eccentric force, the greater the quantity of angular momentum generated
• conservation of angular momentum

  angular momentum is a conserved quantity which remains constant unless an external eccentric force or torque is applied
• angular analogue of Newton's first law of motion

  the angular equivalent of Newton's first law of motion states: a rotating body will continue to turn about its axis of rotation with constant angular momentum unless acted upon by an eccentric or external torque
• fluid mechanics

  • the force of air resistance acts on a body travelling at high velocity through the air, such as a cyclist, sprinter or skier
  • the force of drag acts on a body travelling through the water, such as a swimmer
• reducing air resistance and drag: velocity

  the greater the velocity, the greater the air resistance or drag. track cycling, speed skating, downhill skiing and freestyle swimming are all greatly affected due to the high velocities travelled. velocity cannot be reduced to minimise air resistance or drag and therefore other factors must be considered
• reducing air resistance and drag: frontal cross sectional area

  the larger the frontal cross sectional area, the larger the air resistance or drag. sports such as track cycling and downhill skiing are greatly affected due to the large frontal cross section of the body facing the oncoming air. every effort is made to reduce the size of the frontal cross sectional area to minimise air resistance and drag
• reducing air resistance and drag: streamlining and shape

  the more streamlined or aerodynamic the shape of the body in motion, the lower the air resistance or drag. streamlining is the creation of a smooth air flow around an aerodynamic shape. the more aerodynamic the shape of a body or equipment the lower the air resistance or drag will be. many sports use a tear drop or aerofoil shape, such as a track cyclist, downhill skier or speed skater's helmet
• reducing air resistance and drag: surface characteristics

  the smoother the surface, the lower the air resistance or drag. participants in sports such as swimming, cycling, sprinting and speed skating wear specially engineered clothing to create the smoothest surface possible to reduce the friction between the fluid and body surface
• for example, a downhill skier wanting to reduce air resistance while at a high velocity:

  • minimise the frontal cross sectional area by adopting a low crouched position in the straights and jump sections
  • wear tear drop shaped helmets, and have fins on their gloves and around their boots to create a streamlined shape, easing the air flow around their body
  • wear silky lycra suits to create a smooth surface
• for example, a cyclist wanting to reduce air resistance while at high velocity:

  • lightweight carbon fibre bicycle design with aerodynamic features such as disc wheels and aerodynamic forks to reduce energy expenditure and minimise air resistance
  • aerodynamic riding positions with shoulders forward, a high seat position to tilt the body forwards and narrow handlebars to bring in the hands and elbows to ensure a small frontal cross sectional area
  • aerodynamic helmets with a glossy surface and specialised shape to streamline air flow
  • tight fitting lycra skin suits and shaved body parts
• projectile motion

  movement of a body through the air following a curved flight path under the force of gravity
• projectile

  a body that is launched into the air losing contact with the ground surface, such as a discus or a long jumper
• the horizontal distance travelled by a projectile is affected by four factors:

  1. speed of release
  2. angle of release
  3. height of release
  4. aerodynamic factors (Bernoulli and Magnus)
• speed of release

  the horizontal distance a projectile travels is primarily affected by the speed of release. due to newtons second law of acceleration, the greater the force applied to the projectile, the greater the change in momentum and so acceleration of the projectile into the air. the greater the outgoing speed of the projectile, the further it will travel
• angle of release

  the horizontal distance a projectile travels is affected by the angle of release. based on the projectile being released from the same height, at a angle of release of:

  • 90 degrees: the projectile will accelerate vertically upwards and come straight down travelling 0m
  • 45 degrees: optimal angle to maximise horizontal distance
  • greater than 45 degrees: the projectile reaches peak height too quickly and rapidly returns to the ground
  • less than 45 degrees: the projectile does not achieve sufficient height to maximise the flight time
• height of release

  45 degrees is the optimal angle of release if the release height and landing height are equal. but, if the release and landing height are different, the optimal angle will change:

  • where release height is above landing height e.g., a javelin, optimal angle of release is less than 45 degrees as the projectile already has an increased flight time due to increased height of release
  • where release height is below landing height e.g., a bunker shot in golf, optimal angle of release is more than 45 degrees as the projectile needs an increased flight time to overcome the obstacle
• if weight is the dominant force and air resistance is very small, a parabolic flight path occurs

  • for example, a shot put has a high mass and travels through the air at low velocity, with a relatively low frontal cross sectional area and smooth surface, which makes air resistance negligible
  • the flight path has a parabolic shape symmetrical about its highest point