1. What is Angle of Twist?

The angle of twist (θ) is the angular deformation experienced by a shaft when subjected to torque. It depends on the material properties (shear modulus), shaft geometry (diameter and length), and the applied torque.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( J \) — Polar moment of inertia (m⁴)
• \( \theta \) — Angle of twist (radians)
• \( T \) — Applied torque (N·m)
• \( L \) — Length of shaft (m)
• \( G \) — Shear modulus of material (Pa)
• \( d \) — Diameter of shaft (m)

Explanation: The polar moment of inertia (J) quantifies resistance to torsion, while the angle of twist formula relates all parameters to determine the angular deformation.

3. Importance of Angle of Twist Calculation

Details: Calculating angle of twist is essential in mechanical design to ensure shafts and other components don't deform excessively under torque, which could lead to failure or impaired function.

4. Using the Calculator

Tips: Enter torque in N·m, length in meters, shear modulus in Pascals, and diameter in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is typical shear modulus for steel?
A: For steel, G ≈ 79.3 GPa (79.3 × 10⁹ Pa). Aluminum is about 26 GPa, and copper is about 45 GPa.

Q2: How does diameter affect angle of twist?
A: Since J depends on d⁴, increasing diameter dramatically reduces angle of twist (inverse relationship to the fourth power).

Q3: What's the difference between degrees and radians?
A: 1 radian ≈ 57.3 degrees. The calculator provides both values for convenience.

Q4: When is this calculation not valid?
A: For non-circular cross-sections, composite materials, or when deformations are large enough to exceed elastic limits.

Q5: How to reduce angle of twist in a design?
A: Increase diameter (most effective), use shorter length, choose material with higher shear modulus, or reduce applied torque.