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Published byChester Baker Modified over 9 years ago
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Conservation of Angular Momentum C13, C14
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Basic Definitions… Torque (finally we get some direction!) Use the Right-Hand-Rule to determine the direction of Torque. Curl the fingers of your right hand in the same direction that the object spins - your thumb points in the direction of the angular velocity, angular momentum, torque, acceleration, displacement …. Use VPython as a “vector calculator”!
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Basic Definitions… Angular Momentum Note the fundamental link to the linear world in this form of the expression for angular momentum
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In other words... Angular Momentum can be thought of in many different ways: These all inter-relate and each equation illustrates an aspect of this fundamental idea
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Conservation of Angular Momentum Just as a moving object has linear momentum - a spinning object possesses angular momentum. As long as there are no external torques and the object is in an isolated system, angular momentum is conserved.
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Examples of Conservation of Angular Momentum The figure skater – just Physics? Watch for the relationship between: –Arm movement and rotational speed –Rotational speed and vertical stability
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Examples of Conservation of Angular Momentum The following applet can be used to illustrate conservation of L Neutron stars and PULSARS are nature’s version of the previous two examples! PULSARS
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Angular Momentum and Precession What happens if we try to spin an object that is already spinning? Answer: depending how we do it the result can be counter- intuitive Go to VPython simulation
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Digging Deeper – the math behind precession The slow rotation of a spinning wheel, suspended at only one point is an example of precession. We can easily determine the precession rate:
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re-arrange to give… Example: a 1 kg bicycle wheel of radius 30 cm and spinning at 2 rev/s is suspended from a point 4 cm from the center of the wheel. What is the precession rate?
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Important application - MRI
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