PHYS 17200 Lecture Notes - Lecture 20: Angular Momentum, Angular Velocity

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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
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