Transcript Angular Motion

Biomechanics
• Mechanics of movement:
– vectors and scalars – velocity, acceleration and
momentum/impulse in sprinting
– Newton’s Laws applied to movements –
application of forces in sporting activities
– projectile motion – factors affecting distance,
vector components of parabolic flight
– angular motion – conservation of angular
momentum during flight, moment of inertia
and its relationship with angular velocity.
Copy and label your diagram to show the changing
vertical and horizontal vectors at
the following points:
- the point of release
- the highest point of flight
- the point immediately before landing. (3 marks)
•
•
•
•
•
•
•
•
Point of release
A. Positive vertical component
Highest point
B. No vertical component
Before landing
C. Negative vertical component
D. Equal horizontal component at all three points in flight
Vector arrows must be present and attached to the correct point on
the parabolic curve
Angular Motion
Angular motion is the movement of an object
that is rotating – i.e. movement around an axis.
We usually apply angular motion to athletes
who are rotating such as a gymnast, ice skater
or diver, although it can also be applied to
rotating body parts such as in the long jump.
Recap – AS PE:
What were the names of the 3 axis of rotation,
and where do they pass through the body?
Axis
The body can rotate around 3 axis:
1
1. Longitudinal axis…
… e.g. full twisting jump.
2. Frontal (Anterio-posterior) axis…
3
2
… for lateral rotation (e.g. cartwheel)
3. Transverse axis…
… for forward rotation (e.g forward
roll)
Angular vs Linear Motion
All of the key terms learnt about linear motion
have angular counterparts, including:
Angular Distance
Angular Acceleration
Angular Displacement
Torque / Moment
Angular Speed
Moment of Inertia
Angular Velocity
Angular Momentum
Leave space beneath to include def. for each
Angular Distance and
Displacement
Angular distance is…
…the distance (angle) travelled by an object
rotating around an axis
It is measured in… degrees (˚) or radians (rads).
Angular displacement is…
…the smallest distance (angle) between starting
and finishing positions
It is measured in… degrees (˚) or radians (rads).
Radians
The radian is the ratio between the length of
an arc and its radius. The radian is the
standard unit of angular measure, used in many
areas of mathematics.
As the circumference of
a circle = 2πr = 360˚
1 radian = 360 / 2π
1 rad = 57.3˚
Angular Velocity
Angular velocity is…
…the angle through which a body rotates about
an axis in one second
It is measured in… radians/sec
Degrees must be converted into radians
2π radians = 360°
1 radian = 57.2953 °
1 degree = 0.017453 radian
Angular Acceleration
Angular acceleration is…
…rate of change of angular velocity
It is measured in… radians/sec2
Turning Moments, or Torque
• A moment or torque is the turning effect of a force.
• The size of the moment / torque depends upon the size
of the force and the distance that the force acts from the
axis of rotation (pivot)
• The standard measurement of a
torque is Newton metres (Nm).
• All rotation must start with a
torque.
• This occurs when a force acts
outside the centre of mass of the
body – this is called an eccentric
force
Newton’s Laws of Angular
Motion
Basically the same as his laws on
linear motion, except this time
you’re talking about something
that’s rotating!
Newton’s 1st Law of Angular
Motion
A rotating body will continue to turn about its
axis of rotation with constant angular
momentum unless an eccentric force is
exerted upon it.
This is also known as the ‘law of conservation
of angular motion’
Newton’s 2nd Law of Angular Motion
Angular acceleration is proportional to the
torque (force) causing it and takes place in
the direction in which the torque acts.
Newton’s 3rd Law of Angular Motion
For every torque that is exerted by one body
on another, there is equal and opposite torque
exerted by the second body on the first.
Moment of Inertia
Moment of Inertia (MI) is…
…the resistance of a body to change its state
of rotational / angular motion
It depends on two things:
• Mass – the more massive an object, the
greater the MI
• Distribution of mass around the axis of
rotation
Moment of inertia and mass
MI and Distance
i.e. The further away its mass is away from the
axis of rotation, the
its moment
greater
of inertia and the
force is
more
required to make it spin or stop it spinning if
rotation is already occurring.
This can be simply depicted in the following graph:
Moment
of inertia
Distance of mass from axis
The Moment of Inertia (MI) can be calculated
as follows:
MI = Sum (mass of body x distance from axis
part
of rotation2 )
Or
MI = Σ(mxr2)
Any small difference in the distance of the
mass from the axis has a big effect on MI
- If r doubles, MI increases four times!
- If r increases four-fold, MI increases 16 times!
Seeing it in practice
Angular Momentum
NB/ Linear Momentum is calculated as:
Mo = Mass x velocity
Angular momentum is calculated as the product
of Moment of Inertia (MI) and angular velocity
(ω)
Angular Momentum = MI x ω
Recap - Newton’s 1st Law of
Angular Motion
A rotating body will continue to turn about its
axis of rotation with constant angular
momentum unless an eccentric force is
exerted upon it.
This is also known as the ‘law of conservation
of angular motion’
When an object is mid-flight, angular
momentum must remain constant, unless an
external force acts on the object.
When an object is mid-flight, angular
momentum must remain constant, unless an
external force acts on the object.
As angular momentum = MI x ω (angular velocity),
if, during that flight, MI increases, angular
velocity must decrease, and vise versa.
Therefore by reducing the size of the lever
we increase the speed of the rotation.
The spinning chair experiment…
Application to sport – ice skating
Application to sport – trampoline
The relationship between angular momentum, moment of
inertia and angular velocity are more commonly shown as a
graph and diagram:
1. What external factors will be acting on the diver once they have
taken
off from the board?
Increasing
2. According to Newton’s First Law of Angular Motion, what will happen
Value
to
the angular momentum of the diver from the point of take off
until landing?
3. What happens to the Moment of Inertia (MI) as the diver changes
from a straight to a pike position and back again?
4. What therefore must happen to angular velocity during this change in
body position (remember that Angular Momentum = MI x ω)
5. Sketch lines on the graph to show Angular Momentum, Moment of
Inertia and Angular Velocity.
Time
Example exam question:
Ice skating competitions involve skating programmes that last
approximately five minutes, and may involve spinning movements that
confrom to mechanical principles.
The figure shows an ice skater performing part of
Her routine.
Q. Using the figure explain the mechanical principles that allow
spinning ice skaters to adjust their rate of spin. (6)
Mark scheme:
1. ice is a friction free surface.
2. During rotations, angular momentum remains constant.
3. Angular momentum = moment of inertia x angular velocity
4. Angular momentum. Quantity of motion/rotation
5. Moment of inertia. Spread/distribution of mass around
axis/reluctance to rotate.
6. Angular velocity = speed of rotation
7. Change in moment of inertia leads to change in angular
velocity/speed/spin of rotation.
8. Brings arms/legs closer to/further away from axis of
rotation/body leads to increase/decrease in angular
velocity/speed of rotation/spin.
(n.b. On diagrams mark annotations)