Index for
Chapter 4
Rotational Motion
1. Angular Displacement
- angular displacement
- revolutions
2. Angular Velocity
- radians per second
- \(\omega = {\Delta\theta\over\Delta t}\)
3. Angular Acceleration
- angular acceleration
- \(\alpha=\frac{\Delta\omega}{\Delta t}\)
4. Angular Kinematics
- $$\begin{align}
\omega_f&=\omega_i+\alpha\Delta t &\color{blue}{\hbox{no}\,\Delta \theta}\\
\Delta \theta&=\frac{1}{2}(\omega_i+\omega_f)\Delta t &\color{blue}{\hbox{no}\,\alpha}\\
\Delta \theta&=\omega_i\Delta t+\frac12\alpha\Delta t^2 &\color{blue}{\hbox{no}\,\omega_f}\\
\Delta \theta&=\omega_f\Delta t-\frac12\alpha\Delta t^2 &\color{blue}{\hbox{no}\,\omega_i}\\
\omega_f^2&=\omega_i^2+2\alpha\Delta \theta &\color{blue}{\hbox{no}\,\Delta t}\\
\end{align}$$
5. Linear & Angular Motion
- centripetal acceleration
- tangential acceleration
- \(s=r\Delta\theta\) only if \(\Delta\theta\) is in radians
- \(v=r\omega\) (where \(\omega\) is in rad/s)
- \(a_t=r\alpha\) (where \(\alpha\) is in \(\u{rad/s^2}\))
- \(\vec a=\vec a_c+\vec a_t \qquad a=\sqrt{a_c^2+a_t^2}\)