Biomechanics 3

Learning Outcomes

• Link 5 angular motion terms to linear

equivalents

• Explain Newton’s 3 laws of motion applied

to angular motion

• Explain how a figure skater can speed up

or slow down a spin using the law of the

conservation of angular momentum

Angular Motion

• When a body or part of the body moves in

a circle or part circle about a particular

point called the axis of rotation

• E.g. the giant circle on the high bar in the

men’s Olympic Gymnastics

IMPORTANT TERMINOLOGY

Centre of Gravity / Centre of Mass

“The point at which the body is balanced in all directions”

Centre of Gravity & stability

• The lower the centre of gravity is –the more stable the position

Base of support

• The larger the base of support – the more stable the position

Line of Gravity

• An imaginary line straight down from the centre of gravity / mass

•If the line of gravity is at the centre of the base of support – the position is more stable (e.g. Sumo stance)

•If the line of gravity is near the edge of the base of support – the position is less stable (e.g. Sprint start)

•If the line of gravity is outside the base of support – the position is unstable

Which is the most

stable?

To work out the centre of gravity of a 2D shape-

• Hang the shape from one point & drop a weighted string from any point on the object

• Mark the line where the string drops• Repeat this by hanging the object from

another point• Mark the line again where the string drops• The centre of gravity is where the two

lines cross

Jessica Ennis - London 2012

Moment of force or torque

• The effectiveness of a force to produce

rotation about an axis

• It is calculate – Force x perpendicular

distance from the fulcrum

• Newton metres

• (Fulcrum – think of levers)

• To increase Torque – generate a larger

force or increase distance from fulcrum

Angular Distance

• The angle through which a body has

rotated about an axis in moving from the

first position to the second (Scalar)

• Measured in degrees or radians

Angular Displacement

• The shortest change in angular position. It

is the smallest angle through which a body

has rotated about an axis in moving from

the first to second position

• Vector

• Measure in degrees or radians

• 1 radian = 57.3 degress

• Consider movement

form 1 to 2 clockwise

• Angular Distance –

270o

• Angular

Displacement – 90o

Terminology

Angular speed

• The angular distance

travelled in a certain time.

• Scalar

• Radians per second

Angular Velocity

• The angular displacement

travelled in a certain time.

• Vector quantity

• Radians per second

Angular Acceleration

• The rate of change of angular velocity

• Vector quantity

• Radians per second per second (Rad/s2)

Newton’s First Law - Angular

• “ A rotating body continues to turn about

its axis of rotation with constant angular

momentum unless acted upon by an

external torque.”

• (Law of inertia)

Newton’s Second Law - Angular

• “When a torque acts on a body, the rate of

change of angular momentum experience

by the body is proportional to the size of

the torque and takes place in the direction

in which the torque acts.”

• E.g.Trampolinist – the larger

the torque produced – faster

the rotation for the front

somersault – greater

the change in angular

momentum

Newton’s Third Law - Angular

• “For every torque that is exerted by one

body on another there is an equal and

opposite torque exerted by the second

body on the first.”

• E.g. Diver – wants to do a left-hand twist at take

off – he will apply a downward and right-hand

torque to the diving board – which will produce

an upward and left-hand torque – allowing the

desired movement

Video

• Sochi Winter Olympic Games 2014

• 15 year old - Yulia Lipnitskaya's

Phenomenal Free Program

• Watch – how does she speed up and slow

down in her spins?

Reading task

• Actively read (using highlighters) the

article on the Law of conservation of

Angular momentum

• Write down any key questions for

discussion you have about the topic

• DON’T just say ‘I don’t get it all!’ – Think

precisely what do I not understand

Angular Momentum

• The quantity of angular motion possessed

by a rotating body

• Kgm2/s

• Law of conservation of angular momentum

– for a rotating athlete in flight or a skater

spinning on ice – there is no change in AM

until he or she lands or collides with

another object or exerts a torque on to the

ice with the edge of the blade.

Moment of inertia

• The resistance of a rotating

body to change its state of

angular motion

Angular momentum

= moment of inertia x angular

velocity

Moment does not mean a bit of

time (in this case)

– it is a value

• If the body’s mass is close to the axis of rotation, rotation is easier to manipulate. This makes the moment of inertia smaller and results in an increase in angular velocity.

• Moving the mass away from the axis of rotation slows down angular velocity.

ANGULAR MOMENTUM – MOMENT OF INERTIA (rotational inertia)

Try this on a swivel chair – see which method will allow you to spin at a faster rate? Note what happens when you move from a tucked position (left) to a more open position (right).

High

Low

Angular

Velocity

Moment of

inertia

Questions

Task 1

• Great Britain's Beth Tweddle

won a bronze medal in the

uneven bars in the London

2012 with a routine that

involved many rotational

movements. Explain how a

gymnast can alter their speed

of rotation during flight. (6)

Task 2

• Identify two of Newton’s

Laws of Angular Motion

and explain how these

could be applied to

improve performance in a

sporting activity of your

choice.(4)

Task 3 - A Diver performs a 2 tucked front somersaults in their

dive – draw a diagram/graph and explain the Law of

Conservation of Angular Momentum (4)

Mark Schemes – Beth Tweedle Q.

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Learning Outcomes

• Link 5 angular motion terms to linear

equivalents

• Explain Newton’s 3 laws of motion applied

to angular motion

• Explain how a figure skater can speed up

or slow down a spin using the law of the

conservation of angular momentum