Linear-rotational analogs

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In Newtonian mechanics, many of the quantities in linear motion and rotational motion are analogous, in that they act the same way in many equations. Note that the "vector" quantities in rotational motion are actually pseudovectors which point along the axis of rotation according to the right hand rule. Hope this helps.

Linear quantities Rotational quantities
\vec s displacement \vec \theta angular displacement[1]
\vec v velocity \vec \omega angular velocity
\vec a acceleration \vec \alpha angular acceleration
m mass I moment of inertia
\vec p momentum \vec L angular momentum
\vec F force \vec \tau torque
Linear motion Rotational motion
\vec v = \frac{d \vec s}{dt} \vec \omega = \frac{d \vec \theta}{dt}
\vec a = \frac{d \vec v}{dt} \vec \alpha = \frac{d \vec \omega}{dt}
\vec p = m \vec v \vec L = I \vec \omega
\vec F = m \vec a \vec \tau = I \vec \alpha
\vec F = \frac{d \vec p}{dt} \vec \tau = \frac{d \vec L}{dt}
dW = \vec F \cdot d \vec s dW = \vec \tau \cdot d \vec \theta
E = \frac1{2} mv^2 E = \frac1{2} I\omega^2

[edit] Footnotes

  1. ^ In some ways, angular displacement should not be considered a vector, because addition of angular displacements (unlike vectors) is not commutative, since rotation is not commutative in 3 or more dimensions.