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 350000 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 2.1 s. Find the angular acceleration produced by the drill, assuming it to be constant. Express your answer using two significant figures. alpha = How many revolutions does the drill bit make as it comes up to speed? Express your answer using two significant figures.

Explanation / Answer

a)

Use the equation of motion,

v = u + at

v = final angular speed = 350000 rpm = (350000*2*pi/60) rad/s

u = initial angular speed = 0

a = angular acceleration

t = time taken = 2.1 s

So,  (350000*2*pi/60) = 0 + a*2.1

So, a = 17453.3 rad/s2 = 17453.3/(2*pi) rev/s2 = 2777.8 rev/s2 <------answer

b)

Now, use the equation of motion :

v^2 = u^2 + 2as

So, (350000*2*pi/60)^2 = 0^2 + 2*(17453.3 )*s

So, s = 38484.5 rad

= 38484.5/(2*pi) = 6125 revolutions <---------answerr

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