Cinematica del punto

Il vettore accelerazione

 $\overrightarrow{a_P}$  nello SPAZIO è uguale a ...

•  $\overrightarrow{a_P\ }\ =\ \frac{\text{d}^2s}{\text{d}t^2}\overrightarrow{n\ }+\frac{1}{\rho}\left(\frac{\text{d}s}{\text{d}t}\right)^2\ \overrightarrow{t}$  

•  $\overrightarrow{a_P\ }\ =\ \frac{\text{d}^2s}{\text{d}t^2}\overrightarrow{t\ }+\frac{1}{\rho}\left(\frac{\text{d}s}{\text{d}t}\right)^2\ \overrightarrow{n}$  

•  $\overrightarrow{a_P\ }\ =\ \frac{\text{d}^2s}{\text{d}t^2}\overrightarrow{n\ }+\left(\frac{\text{d}s}{\text{d}t}\right)^2\ \overrightarrow{t}$  

•  $\overrightarrow{a_P\ }\ =\ \frac{\text{d}^2s}{\text{d}t^2}\overrightarrow{t\ }$  

Il vettore accelerazione

 $\overrightarrow{a_P}$  nel piano è uguale a...

•  $\overrightarrow{a_P\ }\ =\ \frac{\text{d}^2\rho}{\text{d}t^2}e^{i\theta}+\rho\ \left(\frac{\text{d}\theta}{\text{d}t}\right)^2\ e^{i\left(\theta+\pi\right)}$  

•  $\overrightarrow{a_P\ }\ =\ \sqrt{\left(\frac{\text{d}^2x_P}{\text{d}t^2}\right)^2+\left(\frac{\text{d}^2y_P}{\text{d}t^2}\right)^2}\overrightarrow{t}$  

•  $\overrightarrow{a_P}\ =\ a_{P^{ }}^t\overrightarrow{t}+a_{P^{ }}^n\overrightarrow{n}$  

•  $\overrightarrow{a_P}\ =\ \frac{\text{d}v_P}{\text{d}t}\overrightarrow{t}\ +\frac{v_P^2}{\rho}\overrightarrow{n}$  

I versori della terna intrinseca sono...

• $\overrightarrow{t}\ =\ \frac{\overrightarrow{v_P}}{\left|\overrightarrow{v_P}\right|}$

• $\overrightarrow{n}\ =\ \overrightarrow{b}\ \times\overrightarrow{t}$

• $\overrightarrow{b}\ =\ \overrightarrow{t}\times\overrightarrow{n}$

• $\overrightarrow{b}\ =\ \overrightarrow{n}\times\overrightarrow{t}$

Il moto rettilineo del punto P nel piano...

• $\overrightarrow{a_P^n\ }=\ 0$

• $\overrightarrow{t}\ =\ \overrightarrow{i}$

• $\overrightarrow{t}\ =\ \cos\left(\alpha\right)\overrightarrow{i}+\sin\left(\alpha\right)\overrightarrow{j}$

• $\overrightarrow{a_P}\ =\ \left(\frac{\text{d}s}{\text{d}t}\right)^2\overrightarrow{t}$

Il moto circolare uniforme del punto P

• $s\ =\ R\omega t$

• $\overrightarrow{v_P\ }\ =\ \rho\frac{\text{d}\theta}{\text{d}t}e^{i\theta}$

• $\overrightarrow{v_P}\ =\ R\omega$

• $\overrightarrow{v_P}\ =\ \frac{\text{d}\rho}{\text{d}t}e^{i\theta}$

Il moto circolare uniforme del punto P

• $\overrightarrow{a_P}\ =\ 0$

• $\overrightarrow{a_P}\ =\ \omega R\overrightarrow{t}+\omega^2R\overrightarrow{n}$

• $\overrightarrow{a_P}\ =\ \omega^2R\overrightarrow{n}$

• $\overrightarrow{a_P}\ =\ \omega R\overrightarrow{t}$

Il moto circolare NON uniforme del punto P...

• $\left|\overrightarrow{a_P}\right|\ =\ \sqrt{\left(\rho\frac{\text{d}^2\theta}{\text{d}t^2}\right)^2+\left(\rho\left(\frac{\text{d}\theta}{\text{d}t}\right)^2\right)^2}$

• $\overrightarrow{a_p}^t\ =\rho\frac{\text{d}^2\theta}{\text{d}t^2}e^{i\left(\theta+\frac{\pi}{2}\right)}\$

• $\overrightarrow{a_p}^n\ =-\rho\left(\frac{\text{d}\theta}{\text{d}t}\right)^2e^{i\theta}\$

• $\overrightarrow{a_p}^n\ =-\rho\left(\frac{\text{d}\theta}{\text{d}t}\right)^2e^{i\left(\theta+\pi\right)}$

Il moto circolare NON uniforme del punto P...

• $\left|\overrightarrow{a_P}\right|\ \ =\ \sqrt{\left(\frac{\text{d}^2s}{\text{d}t^2}\right)^2+\left(\frac{\text{d}s}{\text{d}t}\right)^4}$

• $\left|\overrightarrow{a_P}\right|\ =\ \frac{\text{d}^2x_P}{\text{d}t^2}+\frac{\text{d}^2y_P}{\text{d}t^2}$

• $\left|\overrightarrow{a_P}\right|\ \ =\ \sqrt{\left(\rho\frac{\text{d}^2\theta}{\text{d}t^2}\right)^2+\left(\rho\left(\frac{\text{d}\theta}{\text{d}t}\right)^2\right)^2}$

• $\left|\overrightarrow{a_P}\right|\ \ =\ R\frac{\text{d}^2\theta}{\text{d}t^2}$

Il moto parabolico del punto P ...