The Laws of Motion

The Laws of Motion Newton’s Three Laws of Motion: • Describe the relationship between all the external forces acting on the human body at any time and the resulting motion of the total body • Sir Isaac Newton developed these laws to explain why things move the way they do

Newton’s First Law: Inertia • An object will not change its state of motion (it will continue to be at rest or moving with constant velocity), unless acted upon by a net , external force • For example: because of their large mass, football linemen are difficult to move out of the way

Newton’s Second Law: Acceleration • For linear movements, the acceleration (a) a body experiences is proportional to the force (F) causing it, and takes place in the same direction as the force F = m.a where m is the mass of the body • For angular movements, the angular acceleration of a body is proportional to the moment of force causing it, and takes place in the same direction as the moment of force

Force, Mass, & Acceleration The greater the force applied to a soccer ball that has the same mass, the greater the ball’s acceleration

Force, Mass, & Acceleration cont’d As the soccer ball’s mass increases, it experiences less acceleration from a kick of the same force

Force, Mass, & Acceleration cont’d As the mass of the soccer ball is increased, greater force must be generated if the ball is to have the same acceleration

Impulse, Impact, and Momentum • Momentumis the amount of motion a body possesses • A product of mass and velocity • Impulseis the application of an internal force over a short time period • Impactis the application of an external force over a short time period • Momentum is created by an impulse and is lost through impact • Impulse and impact are both associated with bodies that are changing their state of motion by experiencing large accelerations over relative short time periods • Collision or impact skills can sometimes manipulate the time of contact and reduce the magnitude of the external force • To increase impulse, a sprinter must increase the net external force per step

Newton’s Third Law: Action-Reaction • Every action has an equal and opposite reaction • The two acting forces are equal in magnitude, but opposite in direction • Example: -the sprinter exerts a force onto the blocks, and simultaneously the blocks exert an equal force back onto the sprinter

Projectile Motion • Any airborne object is a projectile, including the human body • The centre of mass of a projectile will follow a parabolic path • The parabolic path followed is determined only as a function of the projectile’s takeoff velocity

Projectile Motion cont. • Objectives of the projectile motion: - maximum vertical distance or height - maximum horizontal distance or range - a combination of both height & range (accuracy)

Maximizing Height and Range • To maximize vertical distance (height), one must maximize the takeoff velocity and take off vertically • To maximize horizontal distance (range), one must maximize the takeoff velocity and take off at an angle of 45 degrees to the horizontal

Air Resistance • Another force acting on a projectile • Will change the state of motion of the projectile and its path

Fluid Dynamics • All athletic events take place in a fluid environment, whether in water (swimming), in air (cycling), or in a combination of both (water polo) • Fluid forces include: drag force and lift force • Drag and lift forces are perpendicular to each other, produce different effects, and are affected by different factors • Flow velocity – the motion of the fluid flowing past an object or the motion of the object through the fluid

Effects of air resistance on a discus Discus with direction of travel and relative flow velocity vectors superimposed Free body diagram of a discus indicating lift, drag, and gravity vectors

Fluid Drag Forces • Two types: Skin-friction and profile drag • Both skin friction and profile drag are proportional to relative flow velocity, cross-sectional area, shape of object, smoothness of surface, and density of liquid

Skin Friction Drag • Caused by the fluid tending to rub (shear) along the surface of the body • Parallel to the flow velocity • The layer of fluid next to the skin sticks to the body; however, the next layer is towed along and therefore slides relative to the innermost layer • The region of relative motion between adjacent layers of fluid particles is called the Boundary Layer • Two types of flow can occur within the boundary layer: laminar flow and turbulent flow

Skin Friction Drag cont. Laminar flow • The smooth, layered, flow pattern of a fluid around an object with no disturbance • Occurs if an object is small, streamlined, smooth, relatively slow and has no rotation

Profile Drag (pressure or form drag) • The main form of drag in skiing, cycling, running, all projectile events, and swimming • Represents the resistive drag against the object • Characterized by turbulent flow in which the pressure on the leading surface of a body is greater than the pressure on the trailing surface

Profile Drag cont. Turbulent flow • Occurs when the velocity of air flow past the object is too fast for the air to follow the contour of the trailing side of the object, causing “back flow” at the surface of the object • This causes a large, turbulent, low-pressure zone to form behind the object • The region of low pressure increases the amount of work done on the object • Profile drag can be reduced by streamlining

Fluid Lift Forces • Always directed perpendicular to the flow velocity • Can be directed upwards(javelin), downwards (racing cars), sideways(sailboats) • Air flows faster over the upper curved surface than the lower flat surface, such that the difference in velocity across the surfaces results in a pressure difference between the two sides • The external force resulting from the pressure difference is perpendicular to the direction of flow velocity, and can change the motion of the object • Bernoulli’s principle-the inverse relationship between flow velocity and pressure

Aerodynamic lift force acting on an airplane wing (Bernoulli’s Principle)

Fluid Lift Forces cont.

Angle of Attack • Refers to the tilt of an object relative to the flow velocity • Can mimic the effects of an airfoil by changing the pressure difference across the surfaces of the object • It is a function of the shape of an object and the flow velocity • If the angle of attack increases too much, it approaches a critical maximum angle (stall angle), beyond which the lift force decreases as the drag force becomes dominant

The Magnus Effect • The pressure difference across opposite sides of an object (which spins about an axis that is not aligned with the flow velocity vector) can generate a change its flight path through a type of lift force known as Magnus force • The changes in flight path are always perpendicular to the flow velocity of the projectile • Topspinrestricts the horizontal distance with no loss in takeoff velocity • Underspin will increase the horizontal distance, time in the air, or accuracy for a given takeoff velocity • Sidespins will curve the ball towards the spinning side

The Magnus Effect The Magnus force is directed from high to low pressure

The ball’s 108 stitches carry a layer of air with them as they spin. That layer makes the air on the bottom of the ball flow faster than the air at the top of the ball which produces the curve ball i.e Magnus effect at work Why a Curveball Curves?

The Laws of Motion