QQuestionPhysics
QuestionPhysics
What is the conversion from RPM (revolutions per minute) to rad/s (radians per second)?
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Answer
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Step 1:: Understand the problem
We need to convert revolutions per minute (RPM) to radians per second (rad/s). To do this, we'll use the following conversion factors: 1 revolution = 2π radians 1 minute = 60 seconds
Step 2:: Convert minutes to seconds
\text{Time (s)} = \text{Time (min)} \times \frac{60 \text{ seconds}}{1 \text{ minute}}
Since there are 60 seconds in a minute, we can convert RPM to rad/s by first converting the time from minutes to seconds:
Step 3:: Set up the conversion equation
\text{W_rad/s} = \text{W_RPM} \times \frac{2\pi \text{ radians}}{1 \text{ revolution}} \times \frac{1 \text{ revolution}}{1 \text{ minute}} \times \frac{1 \text{ minute}}{60 \text{ seconds}}
Now, we can set up the conversion equation using the conversion factors from Step 1 and the time conversion from Step 2:
Step 4:: Simplify the equation
\text{W_rad/s} = \text{W_RPM} \times \frac{\pi}{30} \text{ rad/s}
We can simplify the equation above to get:
Final Answer
The conversion from RPM to rad/s is given by the equation: \text{W_rad/s} = \text{W_RPM} \times \frac{\pi}{30} \text{ rad/s} This equation allows you to convert a rotational speed in RPM to rad/s.
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