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)

Descriptors of linear motion

Graphs of linear motion

Distance/Time

Speed/ Time

Velocity/ Time

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

Axes of rotation

Longitudinal - top to bottom

Transverse- side to side

Frontal- front to back

Descriptors of angular motion

Radians

• the angle through which a body rotates

• Radian = 57.3 degrees

• 6.28 rads in a circle

Factors affecting size of moment of inertia

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

Distribution of mass from the 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

MI directly effects angular velocity:

• high MI = high resistance to rotation = low angular velocity = rate of spin is slow

Conservation of 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

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

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

Applied to a 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 travelled

• speed of release - the greater the force applied, the greater the change in momentum and therefore acceleration, so it will travel a grater 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

• 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

• aerodynamic factors - Bernoulli and Magnus

Flight paths

Parabolic = uniform curve

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

• shot put, football, tennis ball

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

Lift and 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

Spin and Magnus

• topspin, backspin, hook, slice

• the point at which the eccentric force is applied determined which way the object will 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

Topspin Example

• 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

Fluid Mechanics

There are four main factors which affect air resistance and drag.

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

• Velocity - increased velocity = increased drag

• Frontal cross-sectional area - greater cross-sectional area = greater drag

• Streamlining and shape - more aerodynamic = lower drag

• Surface characteristics - smoother surface = less drag