Mouvement circulaire uniformément accéléré

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Cegep1

Mechanics

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165 words

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2 minutes

Mouvement 2D avec des accélérations centripète et tangentielle dont les modules sont constants
MCU + accélération tangentielle
Abbr. MCUA

$$\begin{array}{rl}\overrightarrow{a}& =\overrightarrow{a_c}+\overrightarrow{a_t}\\ a& =\sqrt{a_c^2+a_t^2}\\ |a_t|& =\left|\frac{dv}{dt}\right|\\ \\ s& =r\theta \\ t_t& =r\omega \\ a_t& =r\alpha \\ \\ \omega (t)& =\frac{d\theta }{dt}\\ \alpha (t)& =\frac{d\omega }{dt}\\ \\ \theta (t)& ={\theta }_0+{\omega }_{0}t+\frac{1}{2}\alpha t^2\\ \omega (t)& ={\omega }_0+\alpha t\\ {\omega }^2(t)& ={\omega }_0^2+2\alpha (\theta -{\theta }_0)\\ \theta (t)& ={\theta }_0+\frac{{\omega }_0+\omega (t)}{2}t\end{array}$$

[!example]- ${\omega }_0=3.4\frac{rad}{s},\theta =1.25\ast 2\pi =2.5\pi rad,\alpha =?,t=?$

$$\begin{array}{rl}{\omega }^2(t)& ={\omega }_0^2+2\alpha (\theta -{\theta }_0)\\ 0& ={3.4}^2+2\alpha (2.5\pi -0)\\ a& =-0.7359\dots \frac{rad}{s^2}\end{array}$$$$\begin{array}{rl}\omega (t)& ={\omega }_0+\alpha t\\ 0& =3.4-0.7359\dots t\\ t& \approx 4.620s\end{array}$$

Contributors

Ajitani Hifumi

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