19 lines
847 B
Markdown
19 lines
847 B
Markdown
[[Torque and Rotational Dynamics]]
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# Summary
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* Angular displacement is measured with $\Delta \theta=\theta-\theta_0$
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* Track angular displacement direction with clockwise counterclockwise sign convention
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* Average angular velocity: $w_{avg}=\frac{\Delta\theta}{\Delta t}$
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* Average angular acceleration: $a_{avg}=\frac{\Delta w}{\Delta t}$
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* Rigid system holds shape, but different parts move at different speeds so you can't treat it as a single particle unless COM motion describes rotation well
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* Slope of theta vs time shows angular velocity
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* Slope of angular velocity vs time shows angular acceleration
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* Integral of angular velocity vs time shows Delta theta
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# Angular vs. Linear Motion
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Angular motion equations are similar to linear motion equations.
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$w=w_0+at$
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$\theta=\theta_0+w_0t+\frac{1}{2}at^2$
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$w^2=w^2_0+2a(\theta - \theta_0)$
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