The drill used by most dentists today is powered by a small air-turbine that can

Question

The drill used by most dentists today is powered by a small air-turbine that can operate at angular speeds of 349000 rpm. These drills, along with ultrasonic dental drills, are the fastest turbines in the world - far exceeding the angular speeds of jet engines. Suppose a drill starts at rest and comes up to operating speed in 2.14 s.

A. Calculate the angular acceleration produced by the drill, assuming it to be constant. Give answer in rev/s

B. How many revolutions does the drill bit make as it comes up to speed?

Explanation / Answer

let
v = angular velocity
a = angular acceleration
t = time
dx = angular displacement (theta)

v(i) = 0
v(f) = v = 349000r/m = 20940000r/s
1 revolution = 360 degrees

v = v(i) + at
dx = v(i)t + 1/2at^2

a) v = v(i) + at = at
a = v/t = (20940000r/s)/(2014s) = 9785046.7r/s^2

b) #revolutions = dx/360 = (1/2at^2)/360 = 1/2(9785046.7r/s^2)(2.14s)^2/360 = 62238.33 revolutions

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