# Rotating Bodies - Stress

## Stress in rotating disc and ring bodies

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### Rotation Disc

Stress in a rotating disc can be expressed as

*σ _{z} = ω^{2} r^{2} ρ / 3 *

* = v ^{2} ρ / 3*

* = ( 2 π n / 60)^{2} r^{2} ρ / 3 (1)*

*where *

*σ _{z} = stress (Pa, N/m^{2})*

*ω = angular velocity (rad/s)*

*r = radius of disc (m)*

*ρ = density (kg/m ^{3})*

*π* = 3.14...

*n= revolutions per minute (rpm)*

### Rotation Ring

Stress in a rotating ring can be expressed as

*σ _{z} = ω^{2 }ρ (*

*r*

_{1}^{2}*+ r*

_{1}^{ }*r*

_{2 }*+*

*r*

_{2}^{2}*) / 3 (2)*

*where *

*r _{1} = outer radius of ring (m)*

*r _{2} = inner radius of ring (m)*

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