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?

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 – fasterthe 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