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

37 views1 pages

6 Apr 2015

School

Department

Course

Professor

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