Problems and solutions I

# Then we considered quantities like angular velocity

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Unformatted text preview: anets, stars, solar systems and galaxies. It is also important on the very small scale; in particle accelerators where elementary particles are collided and created, angular momentum is always conserved. More on Rigid Bodies Axes and Origins We began with a discussion of rigid bodies rotating about a fixed axis. Then we considered quantities like angular velocity, angular acceleration, torque and angular momentum as vectors. How are the two points of view related? Torque and angular momentum vectors are ” relative to an origin, where the position vector r is based at the origin. If the origin is chosen as some point on the axis then the vector relative to the axis is just the component in the direction of the axis. The torque about some origin is the vector ” t = r ä F. The torque about the z axis is just the z component of this tz = t where t = r F¶ = r F sin q = r¶ F. Similarly, the angular momentum of a particle relative to an origin ” L = rä p can be written relative to an axis. If the axis is the z axis then L about the axis is just the z component of L about the origin. Lz = L where L = r p¶ = r p sin q = r¶ p. Angular Momentum of a Rigid Body As before, we view our rigid body as a collection of point masses where the perpendicular distance form the axis to mi is ri . Since all the ri are fixed we get the momentum related...
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## This document was uploaded on 02/26/2014 for the course PHYS 2425 at Blinn College.

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