User:Hyperquantization/Equation sandbox

[edit] Rotational Inertia

$I = M R 2$

$I = \frac{1}{2}MR^2$

$I = \frac{1}{12}ML^2$

$I_{pulley} = \frac{1}{2}MR^2$

$I r i n g = M R 2$

$I b r a s s = M R 2$

$I_{disk} = \frac{1}{2}MR^2$

$I_{rod} = \frac{1}{12}ML^2$

$F n e t = m a$

$τ n e t = I α$

$\vec \tau = \vec r \times \vec F$

$x = x_0 + v_0t + \frac{1}{2}at^2$

$\theta = \theta_0 + \omega_0t + \frac{1}{2}\alpha t^2$

$v_\bot = r\omega$

$a_\bot = r\alpha$

Tension (T) in the string: $\begin{align}F_{net} = ma & = mg - T \\ T & = mg - ma\end{align}$