# Angular Motion

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## Angular Motion

Definition - movement of a body or part of a body in a circular path about an axis of rotation

Eccentric force - a force applied outside the centre of mass, resuting in angular motion

Torque - measure of the turning force applied to a body

Angular motion results from eccentric force being applied to a body

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## Principle Axes of Rotation

If eccentric force applied to a body it will rotate around one or more of three principles of rotation

Longitudinal axis:

• runs from top to bottom of body
• e.g. ice skater spinning

Transverse axis:

• runs through sides of body
• e.g. trampolinist somersault

Frontal axis:

• runs from front to back of body (belly button)
• e.g. gymnast performing cartwheel
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## Angular Motion Descriptors

Moment of inertia (MI)

• the resistance of a body to change its state of angular motion or rotation
• moment of inertia = sum of (mass x distribution of the mass from axis of rotation²)
• kgm²

Angular velocity

• the rate of change in angular displacement/rate of rotation
• angular velocity = angular displacement/time taken

Angular momentum

• the quantity of angular motion possessed by a body
• angular momentum = moment of inertia x angular velocity
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## Conservation of Angular Momentum

Conservation of angular momentum - angular momentum is a conserved quantitiy which remains constatn unless an external eccentric force or torque is applied

Once generated angular motion doesn't change throughout a movement - remains constant and therefore conserved

Rotating body will continue to turn about axis of rotation with constant angular momentum unitll acted upon by external force (angular version of Newton's first law)

As angular motion can't be changed once in flight so important to generate as much angular momentum as possible at take-off but can alter moment of inertia + angular velocity throguh changing body position

e.g. description through movement - ice skater triple axel jump

• take off - angular momentum generated by ice skater applying an eccentric force from ice to body
• rotation starts about longitudinal axis
• distribution of mass away from longitudinal axis, MI high, AV low so jump rotating slowly with control
• during flight - mass distributed close to longitudinal axis, MI decreased, AV increased, ice skater spins quickly
• landing preperation - mass distributed away from longitudinal axis, MI increased, AV reduced, rate of spin decreased for landing control
• during landing - ice applies external torque to remove quantity of angular momentum
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