# Initial Length

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Initial Length Formulas

$$\large{ l_i = \frac{ l_f }{ \overrightarrow{\alpha_l} \; \left( T_f \;- \; T_i \right) \;+\; 1 } }$$     (Linear Thermal Expansion Coefficient)

$$\large{ l_i = \frac{ \Delta l }{ \epsilon } }$$     (Strain)

Symbol English Metric
$$\large{ l_i }$$ = initial length $$\large{ft}$$ $$\large{m}$$
$$\large{ l_f }$$ = final length $$\large{ft}$$ $$\large{m}$$
$$\large{ \Delta l }$$ = length differential $$\large{ft}$$ $$\large{m}$$
$$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{1}{F} }$$ $$\large{ \frac{1}{C} }$$
$$\large{ \epsilon }$$  (Greek symbol epsilon) = strain $$\large{ \frac{in}{in} }$$ $$\large{\frac{mm}{mm}}$$
$$\large{ T_f }$$ = final temperature $$\large{F}$$ $$\large{C}$$
$$\large{ T_i }$$ = initial temperature $$\large{F}$$ $$\large{C}$$

Tags: Length Equations