A 7 12inch circular power saw rotates at 4900 revolutions pe

A 7 1/2-inch circular power saw rotates at 4900 revolutions per minute. (Round your answers to two decimal places.)

(a) Find the angular speed of the saw blade in radians per minute.
radians/min

(b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut.
ft/min

Solution

a) we know in 1 complete revolution we have 2 pi radians

so 4900 rev per min = 2*pi*4900 = 30772 rad per minute

b) radius r= 7.50/2 = 3.75 inches

circumference = 2*pi*3.75 = 7.5 pi

so in one revolution each tooth moves 7.5 pi inches

So with 4900 revolutions per minute, each tooth moves 7.5*pi*4900 = 115395 inches per minute