3.2 Types of Motion and Fluid Mechanics

Linear motion

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

• a force is applied to the centre of mass of a body (direct force is applied)

Linear motion descriptor - distance

Total length of the path covered from start to finish

• metres

Linear motion descriptor - displacement

The shortest straight line route from start to finish

• metres

Linear motion descriptor - speed

The rate of change in distance

• speed = distance/ time

• metres per second

Linear motion descriptor - velocity

The rate of change in displacement

• velocity = displacement/ time

• metres per second

Linear motion descriptor - acceleration/ deceleration

The rate of change in velocity

• Acceleration = (final velocity- initial velocity)/ time

• metres per second per second

Angular motion

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

• an eccentric force/ torque is applied to a body, outside of the centre of mass

Angular motion descriptors - moment of inertia

The resistance of a body to change its angular motion or rotation

• MI = mass x distribution of mass from the axis of rotation²

• Kilogram metres²

Angular motion descriptors - angular velocity

The rate of change in angular displacement or rate of rotation

• Angular velocity = angular displacement/ time

• Radians per second

Angular motion descriptors - angular momentum

The quantity of angular motion possessed by a body

• Angular momentum = MI x angular velocity

• Kilogram metres² per second

Radians

• the angle through which a body rotates

• Radian = 57.3 degrees

• 6.28 rads in a circle

Factors affecting MI - mass

• greater mass = greater MI

  • the lower the mass, the easier it is to change the rate of rotation

• sports with a high degree of rotation - e.g. high board diving - are often performed by athletes with a lower mass

Factors affecting MI - distribution of mass from axis of rotation

• the further away the mass is from the axis of rotation, the higher the MI

• the more closely the mass is tucked in around the axis of rotation, the lower the MI

  • a back tuck is easier than a back layout

  • the body will face less resistance in the back tuck, so will rotate quicker

Conservation if angular momentum

• angular momentum, once generated, does not change, unless an eccentric force is applied

• remains constant, and is therefore called a conserved quantity

• this is linked to the angular analogue of Newton’s first law

Angular analogue of Newton’s first law

The Angular Analogue of Newton’s First Law states that a rotating body will continue to turn about an axis of rotation with constant angular momentum unless acted upon by an eccentric force

Conservation of angular motion practical example

At take off, angular momentum is generated by the ice skater applying an eccentric force from the ice to the body. Rotation is about the longitudinal axis. Distribution of mass is away from the longitudinal axis, so MI is high, angular velocity is low and rate of spin is low. During flight, the mass is distributed closer to the axis of rotation, decreasing MI, increasing angular velocity, and increasing rate of spin. During landing, the mass is distributed further away from the axis of rotation, increasing MI, decreasing angular velocity, and decreasing rate of spin

Graph of angular velocity - diver

At take off, angular momentum is generated by an eccentric force from the springboard acting on the body.

Rotation occurs about the transverse axis.

Angular momentum is a conserved quantity and so will remain consistent throughout the movement.

The straight body position which the diver creates during take off distributes the mass away from the axis of rotation - MI is high, angular velocity and rate of spin are low, so the diver rotates slowly.

During flight, the diver will create a tucked body position, which distributes mass close to the axis of rotation - MI is decreased, angular velocity and rate of spin are increased, so the diver rotates quickly.

When the diver prepares to enter the water, they will create a straight body position, which distributes the mass away from the axis of rotation - MI is increased, angular velocity and rate of sin are decreased so the diver rotates slowly.

Projectile motion

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

Factors affecting horizontal distance - speed of release

• the greater the force applied, the greater the change in momentum and therefore acceleration, so it will travel a grater distance

Factors affecting horizontal distance - angle of release

• 90 - accelerate vertically and come back down, travelling 0m

• 45 - optimal angle*

• <45 - reaches peak height to quickly and rapidly returns to the ground

• >45 - does not achieve sufficient height to maximise flight time

Factors affecting horizontal distance - height of release

• 45 is only the optimal angle if the release and landing height are equal - e.g a golf ball

  - if the landing height for the projectile is below release height (javelin and shot put), the optimal angle will be below 45

Factors affecting horizontal distance - aerodynamic factors

consider Bernoulli and Magnus

Flight paths - parabolic

uniform curve

• if weight is the dominant force, with little air resistance

• shot put, football, tennis ball

Flight paths - non-parabolic

unsymmetrical curve

• is air resistance is the dominant force, with little weight

• shuttlecock, discus

Parallelogram of forces

• considers the result of all forces acting on a projectile in flight

• draw a free body diagram, add broken parallel lines, draw a diagonal line from CoM to opposite corner

• if the resultant force is closer to weight it will be parabolic

• if the resultant force is closer to air resistance it will be non-parabolic

Bernoulli

• if an aerofoil is present, extra lift can be produced

• the air parts as the aerofoil travels through the air, the air over the top flows faster than the air under the aerofoil so they meet at the same time

• increased velocity = decreased pressure, so an area of low pressure forms above, and an area of high pressure forms below - creates a pressure gradient and additional lift force

• optimal angle of attack = 17

Downwards lift force

• apply Bernoulli’s principle with an inverted aerofoil

• increases downwards force and helps hold an object, e.g a bike or F1 car, to the track

• the spoiler forces air to travel underneath, which is further, and so needs a higher velocity, creating an area of low pressure below the spoiler, and an area of high pressure above the spoiler - creates a pressure gradient and additional downwards lift force

Types of spin

• Topspin = applied above the centre of mass - rotates downwards - shortens flight path

• Backspin = applied below the centre of mas - rotates upwards - lengthens the flight path

• Hook = applied right of the centre of mass - rotates left - swerves to the left

• Slice = applied left of the centre of mass - rotates right - swerves to the right

Magnus - using topspin

• top of the ball spins against the direction of airflow - creates low velocity and high pressure

• bottom of the ball spins with the direction of airflow - high velocity and low pressure

• creates a pressure gradient and a downwards magnus force from an area of high to low pressure

• magnus force adds weight to the ball so the flight path shortens

Drag

the force that opposes the direction of motion of a body through water or air

Factors affecting drag - velocity

• increased velocity = increased drag

Factors affecting drag - frontal cross-sectional area

• greater cross-sectional area = greater drag

Factors affecting drag - streamlining and shape

• more aerodynamic = lower drag

Factors affecting drag - surface characteristics

• smoother surface = less drag