Torque Transmitted By Shaft Given Polar Moment Of Inertia Calculator

Formula Used:

\[ \tau = \frac{\tau_{max} \times J_{shaft}}{R_{shaft}} \]

Torque Exerted on Wheel:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Torque Transmitted By Shaft?

Torque transmitted by shaft is the rotational force or moment that causes the shaft to twist. It represents the turning effect of force on the axis of rotation and is a crucial parameter in mechanical engineering and shaft design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{\tau_{max} \times J_{shaft}}{R_{shaft}} \]

Where:

\( \tau \) — Torque exerted on wheel (N·m)
\( \tau_{max} \) — Maximum shear stress on shaft (Pa)
\( J_{shaft} \) — Polar moment of inertia of shaft (m⁴)
\( R_{shaft} \) — Radius of shaft (m)

Explanation: This formula calculates the torque capacity of a shaft based on its material properties (maximum shear stress) and geometric properties (polar moment of inertia and radius).

3. Importance of Torque Calculation

Details: Accurate torque calculation is essential for designing shafts that can withstand applied loads without failure. It helps determine the appropriate shaft dimensions and material selection for various mechanical applications.

4. Using the Calculator

Tips: Enter maximum shear stress in Pascals, polar moment of inertia in meters to the fourth power, and radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is polar moment of inertia?
A: Polar moment of inertia is a measure of an object's resistance to torsion and depends on the cross-sectional shape and size of the shaft.

Q2: How does shaft radius affect torque capacity?
A: Torque capacity increases with larger shaft radius since the formula shows torque is inversely proportional to radius.

Q3: What is maximum shear stress?
A: Maximum shear stress is the highest stress value that occurs in the shaft material when subjected to torsional loading.

Q4: When is this calculation most applicable?
A: This calculation is most applicable for solid circular shafts undergoing pure torsion with uniform cross-section.

Q5: Are there limitations to this formula?
A: This formula assumes homogeneous material properties, linear elastic behavior, and applies primarily to circular cross-sections.