What angular velocity (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1,000...
Homework Answers
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.
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:
Thus, the angular velocity is 
.
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