On the relation between angular momentum and angular velocity

Abstract

Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.Students of mechanics usually have difficulties when they learn about the rotation of a rigid body. These difficulties are rooted in the relation between angular momentum and angular velocity, because these vectors are not parallel, and we need in general to utilize a rotating frame of reference or a time dependent inertia tensor. We discuss a series of problems that introduce both difficulties.

Demonstrating the Direction of Angular Velocity in Circular Motion

“…lar acceleration and momentum). 3,4 The current study proposes a physical model to teach the angular velocity vector. The setup described in this study can present a more tangible visualization of the angular velocity vector than the righthand rule allows.…”

Rotating frame analysis of rigid body dynamics in space phasor variables

“…8 Now (13b) will yield  on division by (14). For arbitrary C, the quotient does not have a clean form.…”

“…In other words, the correct lab frame will have its L3 axis oriented with the initial configuration of the o axis. In this specially chosen lab frame, (14) will factor out of (13b) leaving uniform precession. At once the quantity Ω-ν becomes determinate and setting it equal to  we have the precession frequency…”

“…The particular solution features uniform precession at a choice of three frequencies but because of the damping term, the slow precession is expected to be prevalent. The polar angle also decreases exponentially in time and eventually the top becomes vertical; the time constant of this decrease 14 (26) is however not equal to that of the homogeneous solutions. When the top is subjected to a horizontal acceleration in addition to gravity, it eventually points opposite to the direction of the net force plus pseudo force.…”

Um passeio por várias álgebras na descrição do momento angular

“…Essas dificuldades estão relacionadas diretamente com o conceito de momento angular e a velocidade angular. Uma das causas destas dificuldades são conceituais e deve-se ao fato de que as leis que governam a translação e rotação são semelhantes [6,7]. Por outro lado, vários experimentos podem ser feitos para que os alunos possam visualizar e demonstrar o momento angular [8][9][10] ou a conservação do momento angular [11][12][13][14].…”