Question

The drill used by most dentists today is powered by a small air-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 angular speeds of jet engines. Suppose a drill starts at rest and comes up to operating speed in 2.0s .How many revolutions does the drill bit make as it comes up to speed? (Rev)Express your answer using two significant figures.

Answer 1

Answer:

5833.33

Explanation:

$\alpha$ = Angular acceleration

$\theta$ = Number of revolutions

$\omega_i$ = Initial angular speed = 0

t = Time taken = 2 s

Final angular speed

$\omega_f=\dfrac{350000}{60}=5833.33\ rps$

From the equation of rotational motion we have

$\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{5833.33-0}{2}\\\Rightarrow \alpha=2916.665\ rev/s^2$

$\theta=\omega_it+\dfrac{1}{2}\alpha t^2\\\Rightarrow \theta=0\times t+\dfrac{1}{2}\times 2916.665\times 2^2\\\Rightarrow \theta=5833.33\ rev$

The number of revolutions is 5833.33