Question

What is the critical speed(RPM) of the ball mill, if the diameter of the ball mill=500 mm and diameter of the ball 80 mm

A) 65

B) 75

C) 45

D) 55

E) 35

Answer 1

$N_c= \frac{1}{2 \pi}[\frac{g}{R-r}]^{0.5}\\ N_c= \frac{1}{2 \pi}[\frac{9.8*10^3}{500-80}]^{0.5}\\ =\frac{1}{2\pi }\left(\frac{9.8\cdot \:10^3}{500-80}\right)^{\frac{1}{2}}\\ =\frac{5\cdot \:19.6^{\frac{1}{2}}}{21^{\frac{1}{2}}}\\ =\frac{1}{2\pi }\cdot \frac{5\cdot \:19.6^{\frac{1}{2}}}{21^{\frac{1}{2}}}\\ =\frac{22.13594\dots }{28.79317\dots }\\ =0.76879*100\\ =76.9$