Table of Symbols
The symbols used in this document are summarized in the Table of Symbols along with their units. Throughout the document, symbols in bold will represent vectors, and scalars otherwise. The symbols are listed in alphabetical order. For vector quantities, the units shown are for each component of the vector.
| Symbol | Description | Units |
|---|---|---|
| \({a_{\text{x}1}}\) | Horizontal acceleration of the first object | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \({a_{\text{x}2}}\) | Horizontal acceleration of the second object | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \({a_{\text{y}1}}\) | Vertical acceleration of the first object | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \({a_{\text{y}2}}\) | Vertical acceleration of the second object | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \(\boldsymbol{a}\text{(}t\text{)}\) | Acceleration | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \(\boldsymbol{F}\) | Force | \({\text{N}}\) |
| \(g\) | Magnitude of gravitational acceleration | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \(\boldsymbol{g}\) | Gravitational acceleration | \(\frac{\text{m}}{\text{s}^{2}}\) |
| \(\boldsymbol{\hat{i}}\) | Unit vector | – |
| \({L_{1}}\) | Length of the first rod | \({\text{m}}\) |
| \({L_{2}}\) | Length of the second rod | \({\text{m}}\) |
| \(m\) | Mass | \({\text{kg}}\) |
| \({m_{1}}\) | Mass of the first object | \({\text{kg}}\) |
| \({m_{2}}\) | Mass of the second object | \({\text{kg}}\) |
| \({p_{\text{x}1}}\) | Horizontal position of the first object | \({\text{m}}\) |
| \({p_{\text{x}2}}\) | Horizontal position of the second object | \({\text{m}}\) |
| \({p_{\text{y}1}}\) | Vertical position of the first object | \({\text{m}}\) |
| \({p_{\text{y}2}}\) | Vertical position of the second object | \({\text{m}}\) |
| \(\boldsymbol{p}\text{(}t\text{)}\) | Position | \({\text{m}}\) |
| \(\boldsymbol{T}\) | Tension | \({\text{N}}\) |
| \({\boldsymbol{T}_{1}}\) | Tension of the first object | \({\text{N}}\) |
| \({\boldsymbol{T}_{2}}\) | Tension of the second object | \({\text{N}}\) |
| \(t\) | Time | \({\text{s}}\) |
| \(\text{theta}\) | Dependent variables | \({\text{rad}}\) |
| \({v_{\text{x}1}}\) | Horizontal velocity of the first object | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{x}2}}\) | Horizontal velocity of the second object | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{y}1}}\) | Vertical velocity of the first object | \(\frac{\text{m}}{\text{s}}\) |
| \({v_{\text{y}2}}\) | Vertical velocity of the second object | \(\frac{\text{m}}{\text{s}}\) |
| \(\boldsymbol{v}\text{(}t\text{)}\) | Velocity | \(\frac{\text{m}}{\text{s}}\) |
| \({w_{1}}\) | Angular velocity of the first object | \(\frac{\text{rad}}{\text{s}}\) |
| \({w_{2}}\) | Angular velocity of the second object | \(\frac{\text{rad}}{\text{s}}\) |
| \({α_{1}}\) | Angular acceleration of the first object | \(\frac{\text{rad}}{\text{s}^{2}}\) |
| \({α_{2}}\) | Angular acceleration of the second object | \(\frac{\text{rad}}{\text{s}^{2}}\) |
| \({θ_{1}}\) | Angle of the first rod | \({\text{rad}}\) |
| \({θ_{2}}\) | Angle of the second rod | \({\text{rad}}\) |
| \(π\) | Ratio of circumference to diameter for any circle | – |
Table of Symbols