Angular Kinematics of Rigid Body Motion

Abstract

B.L.U.F. (Bottom Line Up Front) Rigid Body Motion (RBM) is a combination of translation and rotation. Rotation Kinematics has “Fundamental Angular Kinematic Relations.” Angular Position θ. Angular Velocity \(\omega = {{d\theta } \over {dt}}\). Angular Acceleration \(\alpha = {{d\omega } \over {dt}} = {{{d^2}\theta } \over {d{t^2}}}\), and \(\alpha = \omega {{d\omega } \over {d\theta }}\). Constant Angular Velocity (speed) \(\theta = {\theta _0} + \omega t\). Constant Angular Acceleration \(\omega = {\omega _0} + \alpha t,\theta = {\theta _0} + {\omega _0}t + {1 \over 2}\alpha {t^2}\), and ω2 = ω 20 + 2α(θ - θ0) These relationships are analogous to the translation relations introduced in Class 1 vol. 1).