Density Of Material Given Radial Stress At Center Of Solid Disc Calculator

Density Formula:

\[ \rho = \frac{8 \times \sigma_r}{\omega^2 \times (3 + \nu) \times r_{outer}^2} \]

Radial Stress (σr):

Pascal

Angular Velocity (ω):

rad/s

Poisson's Ratio (ν):

Outer Radius Disc (router):

meter

Density Of Disc (ρ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Density Formula?

The formula calculates the density of material for a solid disc under radial stress at its center. It relates density to radial stress, angular velocity, Poisson's ratio, and the outer radius of the disc.

2. How Does the Calculator Work?

The calculator uses the density formula:

\[ \rho = \frac{8 \times \sigma_r}{\omega^2 \times (3 + \nu) \times r_{outer}^2} \]

Where:

\( \rho \) — Density of disc (kg/m³)
\( \sigma_r \) — Radial stress (Pascal)
\( \omega \) — Angular velocity (rad/s)
\( \nu \) — Poisson's ratio
\( r_{outer} \) — Outer radius of disc (meter)

Explanation: The formula calculates material density based on the stress distribution in a rotating solid disc, accounting for material properties and rotational dynamics.

3. Importance of Density Calculation

Details: Accurate density calculation is crucial for material selection, structural design, and predicting the behavior of rotating components in mechanical systems.

4. Using the Calculator

Tips: Enter radial stress in Pascal, angular velocity in rad/s, Poisson's ratio (typically between 0.1-0.5), and outer radius in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is radial stress in a rotating disc?
A: Radial stress is the stress component acting perpendicular to the radius of the disc, caused by centrifugal forces during rotation.

Q2: How does angular velocity affect density calculation?
A: Higher angular velocities increase centrifugal forces, which affects the stress distribution and thus the calculated density.

Q3: What is Poisson's ratio and why is it important?
A: Poisson's ratio describes how a material deforms in directions perpendicular to applied stress. It's crucial for accurate stress analysis.

Q4: Are there limitations to this formula?
A: This formula assumes homogeneous material properties, constant thickness, and elastic behavior within the material's limits.

Q5: What are typical density values for engineering materials?
A: Common engineering materials range from about 1000 kg/m³ for plastics to 8000 kg/m³ for steels and 2700 kg/m³ for aluminum.