Rotational Motion

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Laws of Change

Differential Form

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\begin

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[ \frac

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= \alpha ]
[\frac

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= \omega]
\end

______

Integral Form

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\begin

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[ \omega_

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= \omega_

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+\int_{t_{i}}^{t_{f}} \alpha \;dt]
[ \theta_

= \theta_

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+\int_{t_{i}}^{t_{f}} \omega\;dt]\end

Note the analogy between these Laws of Change and those of the

One-Dimensional Motion (General) model. Thus, for the case of constant angular acceleration, the integral form of these Laws are equivalent to:

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\begin

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[ \omega_

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= \omega_

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+ \alpha(t_

-t_

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)]
[ \theta_

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= \theta_

+ \frac

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(\omega_

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+\omega_

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)(t_

-t_

)]
[ \theta_

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= \theta_

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+ \omega_

(t_

-t_

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) +\frac

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\alpha(t_

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-t_

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)^

]
[ \omega_

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^

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=\omega_

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^

+ 2\alpha(\theta_

-\theta_

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)]\end