Question

The drill used by most dentists today is powered by a smallair-turbine that can operate at angular speeds of 350000{\rm rpm}. These drills, along with ultrasonic dental drills,are the fastest turbines in the world-far exceeding the angularspeeds of jet engines. Suppose a drill starts at rest and comes upto operating speed in 1.9 s.

Find the angular acceleration produced by thedrill, assuming it to be constant.
α=
How many revolutions does the drill bit makeas it comes up to speed?
\Delta \theta=

Answer 1

α = 3070rev/s^2

θ = 5541.66 revolutions

Step-by-step explanation:

Given;

Operating angular speed w = 350000 rpm

time t = 1.9s

Angular acceleration = change in angular speed/time

Angular acceleration=350000rpm×1/60 min/sec ÷ 1.9s

Angular acceleration α = 3070rev/s^2

Number of revolutions θ = 1/2 × α × t^2

Since initial angular speed is zero

Substituting the values;

θ = 1/2 × 3070 × 1.9^2

θ = 5541.66 revolutions