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Dental Turbine

Dental Turbine
Two questions based on Angular Acceleration, Please help.?

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.

1)Find the angular acceleration produced by the drill, assuming it to be constant.
2)How many revolutions does the drill bit make as it comes up to speed?

Let:
w be the angular speed at time t,
w0 be the initial angular speed,
alpha be the angular acceleration,
theta be the angle turned.

1.
w = alpha t
alpha = w / t
= (3.5 * 10^5 * 2pi / 60) / 2.1
= 1.75 * 10^4 rad/s^2.

2.
theta = t(w0 + w) / 2
= (2.1 / 60)(0 + 3.5 * 10^5) / 2
= 6125 rev.

Testimonial - Dr Willard


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