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Rotational Analogies

It is, however, worth remembering that all the now-familiar [?] paradigms and equations of Mechanics come in ``rotational analogues:''
LINEAR
VERSION
ANGULAR
VERSION

NAME
x $\theta$ angle
$\dot{x} \equiv v$ $\dot{\theta} \equiv \omega$ $\textstyle \parbox{1.25in}{\raggedright angular velocity}$
$\ddot{x} \equiv \dot{v} \equiv a$ $\ddot{\theta} \equiv \dot{\omega} \equiv \alpha$ $\textstyle \parbox{1.25in}{\raggedright angular acceleration}$
m IO $\textstyle \parbox{1.25in}{\raggedright moment of inertia}$
$p = m \, v$ $L_O = I_O \omega$ $\textstyle \parbox{1.25in}{\raggedright angular momentum}$
F $\tau_O$ torque
$\dot{p} = F$ $\dot{L}_O = \tau_O$ SECOND LAW
$T = {1\over2} m v^2$ $T = {1\over2} I_O \omega^2$ $\textstyle \parbox{1.25in}{\raggedright rotational kinetic energy}$
$dW = F \, dx$ $dW = \tau d\theta$ $\textstyle \parbox{1.25in}{\raggedright rotational work}$
F = - k x $\tau = - \kappa \theta$ $\textstyle \parbox{1.25in}{\raggedright torsional spring law}$
$V_s = {1\over2} k \, x^2$ $V_s = {1\over2} \kappa \, \theta^2$ $\textstyle \parbox{1.25in}{\raggedright torsional potential energy}$


next up previous
Next: Statics Up: Torque and Angular Momentum Previous: A Moment of Inertia, Please!
Jess H. Brewer
1998-10-08