Index for
Chapter 4
Rotational Motion

1. Angular Displacement

• angular displacement
• revolutions

2. Angular Velocity

• radians per second
• $\omega =\frac{\mathrm{\Delta }\theta }{\mathrm{\Delta }t}$

3. Angular Acceleration

• angular acceleration
• $\alpha =\frac{\mathrm{\Delta }\omega }{\mathrm{\Delta }t}$

4. Angular Kinematics

• $$\begin{array}{rlr}{\omega }_f& ={\omega }_i+\alpha \mathrm{\Delta }t& \text{no}\mathrm{\Delta }\theta \\ \mathrm{\Delta }\theta & =\frac{1}{2}({\omega }_i+{\omega }_f)\mathrm{\Delta }t& \text{no}\alpha \\ \mathrm{\Delta }\theta & ={\omega }_i\mathrm{\Delta }t+\frac{1}{2}\alpha \mathrm{\Delta }{t}^2& \text{no}{\omega }_f\\ \mathrm{\Delta }\theta & ={\omega }_f\mathrm{\Delta }t-\frac{1}{2}\alpha \mathrm{\Delta }{t}^2& \text{no}{\omega }_i\\ {\omega }_f^2& ={\omega }_i^2+2\alpha \mathrm{\Delta }\theta & \text{no}\mathrm{\Delta }t\end{array}$$

5. Linear & Angular Motion

• centripetal acceleration
• tangential acceleration
• $s=r\mathrm{\Delta }\theta$ $\mathit{only}$ if $\mathrm{\Delta }\theta$ is in radians
• $v=r\omega$ (where $\omega$ is in rad/s)
• $a_t=r\alpha$ (where $\alpha$ is in $\mathrm{rad}/{\mathrm{s}}^2$)
• $\overrightarrow{a}={\overrightarrow{a}}_c+{\overrightarrow{a}}_{t}a=\sqrt{a_c^2+a_t^2}$

6. Assessment Objectives

7. Angular Displacement

8. Angular Velocity