PHYS 17200 Lecture Notes - Lecture 20: Angular Momentum, Angular Velocity
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6 Apr 2015
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PHYS 17200 - Modern Mechanics - Lecture 20_Angular Momentum Principle
Angular Momentum: Principle Definitions
● Rotational Angular Momentum
○ I = m1r2 + m2r2 + m3r2 +m4r2 + …
○ Lrotational = I * ω = (Inertia * angular velocity)
■ analogous to: p = m*v
○ Lrotational = r1 x p1 + r2 x p2 + r3 x p3 + ...
● Translational Angular Momentum
○ Ltranslational = rcm x p (cm = center of mass)
=> LA = Ltranslational + Lrotational
Rotational Kinetic Energy
● Krotational = ½ * m * ωi2
● Energy of a rotating object in motion
● Can be affected by two components as listed above: Rotational Angular Momentum and
Translational Angular Momentum
Torque
● Rotational Force
○ rA x Fnet = τA
○ ∆LA = (rA x Fnet)∆t = τA∆t
Three Fundamental Principles
● Momentum Principle
○ If external forces: momentum changes
○ If no external forces: Momentum of system is constant
● Angular Momentum Principle
○ If external torques: angular momentum changes
○ If no external torques: Angular momentum of system is constant
● Energy Principle
○ If work is done: energy of system changes
○ If no work is done: Energy of system is constant