Question

What angular velocity (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1,000 times gravity at a radius arm of 15.0 cm?

Answer 1

Concepts and reason

The concepts used for solving this problem are the angular velocity and acceleration.

First, use the formula for the acceleration and derive the expression for angular velocity.

Then, substitute the variables and find the value of angular velocity.

Fundamentals

The expression for angular acceleration is given below:

Here, is the angular acceleration, is the radius of the arm, and is the angular velocity.

The relationship between and is given below:

The expression for angular acceleration is given below:

Rearrange the variables and find out the equation for angular velocity.

The acceleration is 1000 times the acceleration due to gravity. Therefore:

Here, is the acceleration due to gravity.

Substitute for .

The angular acceleration is given below:

Substitute for and for .

The relationship between and is given by

Therefore, convert to as follows:

Ans:

Thus, the angular velocity is .