Page Description Equation
77 displacement \[ \Delta\vect{r}=\vect{r}_f-\vect{r}_i \]
77 average velocity \[ \overline{\vect{v}}=\frac{\Delta\vect{r}}{\Delta t} \]
78 velocity \[ \vect{v}=\lim\limits_{\Delta t\rightarrow0}{\frac{\Delta\vect{r}}{\Delta t}=\frac{d\vect{r}}{dt}} \]
79 average acceleration \[ \overline{\vect{a}}=\frac{\Delta\vect{v}}{\Delta t}=\frac{\vect{v}_f-\vect{v}_i}{t_f-t_i} \]
79 acceleration \[ \vect{a}=\lim\limits_{\Delta t\rightarrow0}{\frac{\Delta\vect{v}}{\Delta t}=\frac{d\vect{v}}{dt}} \]
79 position vector \[ \vect{r}=x\vect{i}+y\vect{j} \]
79 velocity vector \[ \vect{v}=v_x\vect{i}+v_y\vect{j} \]
80 kinematic equation \[ \begin{align*} \vect{v}_f &=\vect{v}_i+\vect{a}t\\ v_{x_f} &=v_{x_i}+a_xt\\ v_{y_f} &=v_{y_i}+a_yt \end{align*} \]
80 kinematic equation \[ \Delta\vect{r}=\overline{\vect{v}}t=\frac{1}{2}\left(\vect{v}_i+\vect{v}_f\right)t \]
80 kinematic equation \[ \Delta\vect{r}=\vect{v}t+\frac{1}{2}\vect{a}t^2 \]
80 kinematic equation \[ \vect{v}_f^2-\vect{v}_i^2=2\vect{a}\Delta\vect{r} \]
82 projectile initial velocity, where
$v_i=\text{initial speed}$
$\theta_i=\text{launch angle}.$ 		\[ \vect{v}_i=v_i\cos{\theta_i}\,\vect{i}+v_i\sin{\theta_i}\,\vect{j} \]
83 projectile position vector \[ \vect{r}=\vect{v}_it+\frac{1}{2}\vect{g}t^2 \]
85 projectile time to reach peak \[ t_{\mathrm{peak}}=\frac{v_i\sin{\theta_i}}{g} \]
85 projectile maximum height \[ h=\frac{v_i^2\sin^2{\theta_i}}{2g} \]
85 projectile horizontal range \[ R=\frac{v_i^2\sin{2\theta_i}}{g} \]
tangential acceleration \[ a_t=\frac{d\left|v\right|}{dt}=\frac{dv}{dt} \]
radial acceleration \[ a_r=\frac{v^2}{r}\ \ \left[\frac{\mathrm{L\ }}{\ \mathrm{T}^2}\right] \]
94 acceleration in terms of tangential and radial acceleration. See figure 4.18 p. 94. \[ \begin{align*} \vect{a} &=\vect{a}_t+\vect{a}_r\\ &=\frac{dv}{dt}\hat{\vect{\theta}}-\frac{v^2}{r}\hat{\vect{r}} \end{align*} \]
magnitude of acceleration \[ a=\sqrt{a_r^2+a_t^2} \]
angle between acceleration and position. That is, between $\vect{a} \text{ and } \vect{r}$ \[ \phi=\tan^{-1}{\frac{a_t}{a_r}} \]
Galilean transformation, relative position of inertial frames \[ \vect{r}^\prime=\vect{r}-\vect{v}_0t \]
Galilean transformation, relative velocity of inertial frames \[ \vect{v}^\prime=\vect{v}-\vect{v}_0 \]
Galilean transformation, relative acceleration of inertial frames \[ \vect{a}^\prime=\vect{a} \]
tangential velocity \[ \]
radial velocity \[ \]
Velocity \[ \]