Angle of Twist Calculator

Formula

The formula to calculate the Angle of Twist (α) is:

\[ \alpha = \frac{T \cdot L}{J \cdot G} \]

Where:

\( \alpha \) is the Angle of Twist (radians)
\( T \) is the Torque applied (N·m)
\( L \) is the Length (m)
\( J \) is the Polar Moment of Inertia (m⁴)
\( G \) is the Shear Modulus (N/m²)

What is Angle of Twist?

An angle of twist is defined as the measure of the amount of twist in radians an object undergoes when subjected to a torque. It is an important parameter in mechanical engineering, particularly in the analysis of torsional stress and deformation in shafts and other structural elements.

Example Calculation

Let's assume the following values:

Torque (T) = 500 N·m
Length (L) = 2 m
Polar Moment of Inertia (J) = 0.0001 m⁴
Shear Modulus (G) = 80,000 N/m²

Using the formula to calculate the Angle of Twist:

\[ \alpha = \frac{500 \cdot 2}{0.0001 \cdot 80000} = \frac{1000}{8} = 125 \text{ radians} \]

The Angle of Twist is 125 radians.