Kinematics of rotational motion
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angular displacement $\theta$, in radians
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angular velocity $\omega$, in rad/s
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angular acceleration $\alpha$, in rad/s2
Summary of kinematics, for $\alpha=\mbox{const}$
\[
\begin{array}{l}
\omega = \omega_0 + \alpha t \\
\overline{\omega} = {1\over2} \, (\omega+\omega_0) \\
\theta = \overline{\omega} \, t = {1\over2} \, (\omega+\omega_0)t \\
\theta = \omega_0t + {1\over2}\alpha t ^2
\end{array}
\]
Rolling without slipping $v_t=\omega \, r$, $a_t=\alpha \, r$
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$\omega,\alpha$ - angular velocity and acceleration describe rotation of the whole object
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$v_t, a_t$ - tangential velocity and acceleration describe the motion of one point on the object
Centripetal acceleration for a uniform rotation
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$a_c$ - describes a change in the direction of $\vec{V}$ ($\alpha=0$ means $a_t=0$)
\[
a_c = {{V^2}\over r}= \omega^2 r, \qquad \vec{a_c} \> \bot \> \vec{V}
\]
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\( \vec{a_c} \) is centripetal, i.e. toward the centre of rotation
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