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- 1. Biomechanics 3
- 2. 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
- 3. 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
- 4. IMPORTANT TERMINOLOGY
- 5. Centre of Gravity / Centre of Mass “The point at which the body is balanced in all directions”
- 6. Centre of Gravity & stability • The lower the centre of gravity is – the more stable the position
- 7. Base of support • The larger the base of support – the more stable the position
- 8. 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
- 9. Which is the most Which is the most stable? stable?
- 10. 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
- 11. Jessica Ennis - London 2012
- 12. 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
- 13. 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
- 14. 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
- 15. • Consider movement form 1 to 2 clockwise • Angular Distance – o 270 • Angular Displacement – 90o
- 16. 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
- 17. Angular Acceleration • The rate of change of angular velocity • Vector quantity • Radians per second per second (Rad/s 2)
- 18. 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)
- 19. 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
- 20. 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
- 21. 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.
- 22. 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
- 23. ANGULAR MOMENTUM – MOMENT OF INERTIA (rotational inertia) • 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. 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).
- 24. High Moment of inertia Low Angular Velocity
- 25. Questions Task 1 Task 2 • Explain how a sprinter’s • Explain how a figure stability changes through the skater can change their three phases of a sprint start: speed of rotation on a “on your marks”, “set”, bang” jump – to change the (6) move from a single rotation to a double or • A Diver performs a 2 tucked triple rotation (4) front somersaults in their dive – draw a diagram/graph and explain the Law of Conservation of Angular Momentum (4)
- 26. 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

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