# peripheral velocity

## Solution to Problem 140 Pressure Vessel

**Problem 140**

At what angular velocity will the stress of the rotating steel ring equal 150 MPa if its mean radius is 220 mm? The density of steel 7.85 Mg/m^{3}.

**Solution 140**

$CF = M \omega^2 \bar x$

$M = \rho V = \rho A \pi R$

$x = 2R / \pi$

Thus,

$CF = \rho A \pi R \omega^2 (2R / \pi)$

## Solution to Problem 139 Pressure Vessel

**Problem 139**

Find the limiting peripheral velocity of a rotating steel ring if the allowable stress is 20 ksi and steel weighs 490 lb/ft^{3}. At what revolutions per minute (rpm) will the stress reach 30 ksi if the mean radius is 10 in.?