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 2.0 .

How many revolutions does the drill bit make as it comes up to speed? (Rev)

Express your answer using two significant figures.

Answer 1

Concepts and reason

The concepts used to solve this problem are angular acceleration and angular displacement.

First, find angular acceleration by using the relation between angular acceleration and angular velocity.

Then, find angular displacement by using the relation between angular displacement, angular velocity, angular acceleration and time.

Fundamentals

The formula for angular acceleration is given by,

Here, is the angular acceleration, is the final angular velocity, is the initial angular velocity, and is the time.

The formula for angular displacement is given by

Here, is the time, is the displacement at time , is the displacement at time , is the initial angular velocity, and is the angular acceleration.

The formula for angular acceleration is given by,

Substituting for , for , and for .

The formula for angular displacement is given by,

Modifying the equation for angular displacement,

$109+1°m=(°0–0) $

is the angular displacement between time and .

Substituting for and for and for .

Expressing the answer in two significant figures

Ans:

The drill bit makes .