# Template:Physeq1/RotationalLinearAnalogyTable

The following table refers to rotation of a rigid body about a fixed axis: $\mathbf {s}$ is arclength, $\mathbf {r}$ is the distance from the axis to any point, and $\mathbf {a} _{\mathbf {t} }$ is the tangential acceleration, which is the component of the acceleration that is parallel to the motion. In contrast, the centripetal acceleration, $\mathbf {a} _{\mathbf {c} }=v^{2}/r=\omega ^{2}r$ , is perpendicular to the motion. The component of the force parallel to the motion, or equivalently, perpendicular, to the line connecting the point of application to the axis is $\mathbf {F} _{\perp }$ . The sum is over $\mathbf {j} \ =1\ \mathbf {to} \ N$ particles or points of application.
Displacement = $\mathbf {x}$ Angular displacement = $\theta$ $\theta =\mathbf {s} /\mathbf {r}$ Velocity = $\mathbf {v}$ Angular velocity = $\omega$ $\omega =\mathbf {d} \theta /\mathbf {dt} =\mathbf {v} /\mathbf {r}$ Acceleration = $\mathbf {a}$ Angular acceleration = $\alpha$ $\alpha =\mathbf {d} \omega /\mathbf {dt} =\mathbf {a_{\mathbf {t} }} /\mathbf {r}$ Mass = $\mathbf {m}$ Moment of Inertia = $\mathbf {I}$ $\mathbf {I} =\sum \mathbf {m_{j}} \mathbf {r_{j}} ^{2}$ Force = $\mathbf {F} =\mathbf {m} \mathbf {a}$ Torque = $\tau =\mathbf {I} \alpha$ $\tau =\sum \mathbf {r_{j}} \mathbf {F} _{\perp }\mathbf {_{j}}$ Momentum= $\mathbf {p} =\mathbf {m} \mathbf {v}$ Angular momentum= $\mathbf {L} =\mathbf {I} \omega$ $\mathbf {L} =\sum \mathbf {r_{j}} \mathbf {p} \mathbf {_{j}}$ Kinetic energy = ${\frac {1}{2}}\mathbf {m} \mathbf {v} ^{2}$ Kinetic energy = ${\frac {1}{2}}\mathbf {I} \omega ^{2}$ ${\frac {1}{2}}\sum \mathbf {m_{j}} \mathbf {v_{j}} ^{2}={\frac {1}{2}}\sum \mathbf {m_{j}} \mathbf {r_{j}} ^{2}\omega ^{2}$ 