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BIOMECHANICS Angular Motion

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The same quantities used to explain linear motion are applied to angular motion. In rotating bodies they take on there angular form : - ANGULAR DISPLACEMENTANGULAR DISPLACEMENT ANGULAR VELOCITYANGULAR VELOCITY ANGULAR ACCELERATIONANGULAR ACCELERATION

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ANGULAR DISPLACEMENT – Distance of a body rotating around an axis, measured in degrees (1 complete rotation is 360 o ) ANGULAR VELOCITY – The angle through which the body rotates about an axis in 1 second. E.G A trampolinist performing a tucked back somersault turns through 360 o in 2 seconds. What is the resulting angular velocity? ANGULAR ACCELERATION – The rate of change of angular velocity.

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Moment of Inertia An objects resistance to rotational change. An objects resistance to rotational change. The moment of inertia (MI) is determined by its mass and the distribution of its mass around the axis and rotation. PRACTICAL : - Whilst sitting on the hall floor see how many times you can spin round 360 o with one push!

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You should have found that when you have a wider shape you spin a lot slower and therefore less times. When you tuck in you should have found that you spin a lot faster and do more rotations. (Why is this?) Where the objects mass is concentrated about the axis, the lower the moment of inertia and the greater the angular velocity e.g. when tucking in whilst spinning. Can you think of any other sporting examples? Gymnastics – Somersaults Trampolining Diving Figure Skating

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The further the objects mass is away from the axis the greater its moment of inertia and the slower the rate of rotation, the more force required to make it rotate and stop rotating. (See page 204 in Sport & PE for differences in MI’s)

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ANGULAR MOMENTUM: - This is the product of AV x MI This relates to Newtons 1 st Law i.e. an object will continue to rotate with a constant angular momentum unless acted on by a net force. If MI increases, AV decreases and vice versa. Therefore Angular momentum is conserved and remains the same. TASK!! Copy the graph from the next slide and add onto it the lines representing: - Angular Momentum Angular Velocity Moment of Inertia Explain the shape of the 3 curves you have drawn and the reasons behind them.

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Time (s) Angular Momentum Moment of Inertia Angular Velocity

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ANSWERS! Angular momentum remains constant during the flight. There are no external forces acting The moment of Inertia decreases (in tuck phase) Because of reduction in distribution/spread of mass. Angular velocity increases (during tuck phase) Angular momentum = angular velocity x moment of inertia Another example question? 1.Explain the mechanical principles that allow spinning ice skaters to adjust their rate of spin. (6 Marks)

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ANSWER! -Ice may be regarded as a friction free surface/friction is negligible. -During spins angular momentum remains constant; -Angular momentum is the quantity of rotation; -Angular momentum = AV X MI; -Angular velocity = rate of spin/how faster skater spins; -Moment of inertia = distribution/spread of mass around axis; -Changing/reducing moment of inertia affects/ increases angular velocity; -Skater brings arms into body allowing rate of spin to increase.

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