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# Rotating Bodies - Stress

### Stress in a Rotating Disc

Stress in a rotating disc can be calculated as

σ z = ω2r2ρ / 3

= v2ρ / 3

= ( 2 π n / 60)2r2ρ / 3 (1)

where

σ z = stress (Pa, N/m2)

r = radius of disc (m)

ρ = density (kg/m3 )

π = 3.14...

n= revolutions per minute (rpm)

.

### Stress in a Rotating Ring

Stress in a rotating ring can be calculated as

σ z = ω2ρ ( r12+ r1 r2+ r2 2 ) / 3                     (2)

where

r1 = outer radius of ring (m)

r2= inner radius of ring (m)

For a thin ring the equation can be simplified to

σ z = ω2ρ r                    (3)

where

r  = mean radius of ring (m)

.

### Design Stress for materials used in Flywheels

Design Stress Flywheel Materials
MaterialDensity
(kg/m3 )
Typical Design Stress
( MPa)
Aluminum alloy 2700
Birch plywood 700 30
Composite carbon fiber - 40% epoxy 1550 750
E-glass fiber - 40% epoxy 1900 250
Kevlar fiber - 40% epoxy 1400 1000
Maraging steel 8000 900
Titanium Alloy 4500 650
"Super paper" 1100
S-glass fiber/epoxy 1900 350

## Related Topics

### • Dynamics

Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.

## Related Documents

### Centripetal and Centrifugal Acceleration Force

Forces due to circular motion and centripetal / centrifugal acceleration.

### Flywheels - Kinetic Energy

The kinetic energy stored in flywheels - the moment of inertia.

### Stress

Stress is force applied on cross-sectional area.

### Stress in Thick-Walled Cylinders or Tubes

Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure.

### Stress in Thin-Walled Cylinders or Tubes

Hoop and longitudinal stress thin-walled tubes or cylinders.

### Stress, Strain and Young's Modulus

Stress is force per unit area - strain is the deformation of a solid due to stress.

### Young's Modulus, Tensile Strength and Yield Strength Values for some Materials

Young's Modulus (or Tensile Modulus alt. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.

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