Biomechanics 3

Learning Outcomes

• Link 5 angular motion terms to linear

equivalents

• Describe centre of gravity/mass

• 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

Movement 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

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

• Explain how a sprinter’s

stability changes through the

three phases of a sprint start:

“on your marks”, “set”, bang”

(6)

• 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)

Task 2

• Explain how a figure

skater can change their

speed of rotation on a

jump – to change the

move from a single

rotation to a double or

triple rotation (4)

Learning Outcomes

• Link 5 angular motion terms to linear

equivalents

• Describe centre of gravity/mass

• 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