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