Stress Rotation Disc Ring Body

Overview

Engineering reference data for Stress Rotation Disc Ring Body in mechanics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Work

$W = Fd\cos\theta$

Work = force × displacement × cos(angle).

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Potential Energy

$E_p = mgh$

Gravitational potential energy.

Variables

Formulas

Stress in a Rotating Disc

The stress ($\sigma_z$) induced in a solid rotating disc is given by: $\sigma_z = \frac{\omega^2 r^2 \rho}{3} = \frac{v^2 \rho}{3} = \frac{(2 \pi n / 60)^2 r^2 \rho}{3}$

Variables:

• $\sigma_z$: Stress (Pa, N/m²)
• $\omega$: Angular velocity (rad/s)
• $r$: Radius of the disc (m)
• $\rho$: Density of the material (kg/m³)
• $v$: Tangential velocity ($v = \omega r$, m/s)
• $n$: Rotational speed (revolutions per minute, rpm)

Stress in a Rotating Ring

For a rotating ring with an inner radius $r_2$ and outer radius $r_1$, the stress ($\sigma_z$) is: $\sigma_z = \frac{\omega^2 \rho (r_1^2 + r_1 r_2 + r_2^2)}{3}$

For a thin ring, where the wall thickness is small compared to the mean radius $r = (r_1 + r_2)/2$, this simplifies to: $\sigma_z = \omega^2 \rho r^2$

Variables:

• $r_1$: Outer radius of the ring (m)
• $r_2$: Inner radius of the ring (m)
• $r$: Mean radius of a thin ring (m)

Interactive Charts

References

• Original Source