Rotating Bodies - Stress

Stress in a Rotating Disc

Stress in a rotating disc can be calculated as:

σz = ω² r² ρ / 3

Or alternatively:

σz = v² ρ / 3

Or using RPM:

σz = (2π n / 60)² r² ρ / 3

Where:

• σz = stress (Pa, N/m²)
• ω = angular velocity (rad/s)
• r = radius of disc (m)
• ρ = density (kg/m³)
• v = tangential velocity (m/s)
• n = revolutions per minute (rpm)

Stress in a Rotating Ring

Stress in a rotating ring can be calculated as:

σz = ω² ρ (r₁² + r₁r₂ + r₂²) / 3

Where:

• r₁ = outer radius of ring (m)
• r₂ = inner radius of ring (m)

For a thin ring, the equation simplifies to:

σz = ω² ρ r²

Where:

• r = mean radius of ring (m)