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nccaitlin91 · Mar 26, 2013, 11:39 AM

A wind generator has blades with a radius of 24.5 meters. The blade is turning at an angular velocity of 17.0 rpm. What is the blade's rotational velocity in radians per second?

What equation do I use to solve for this problem? Thanks!

ebaines · Mar 26, 2013, 01:28 PM

You need to convert revolutions per minute first to revolutions per second, then convert that to radians per second. There are 60 seconds in a minute so to convert RPM to revolutions per second multiply by 1/60 min/sec:

$<br /> 17 \frac {rev}{min} \times \frac {1\ Min}{60 \ Sec} = 17 \frac {rev}{\cancel {min}} \times \frac {1\ \cancel{min}}{60 \ sec} = \frac {17}{60} \frac {rev}{sec}<br />$

Next - do you know how many radians are in a full circle? Multiply the above by that factor to get the answer in radians/sec.

nccaitlin91 · Mar 27, 2013, 07:20 AM

2pi*r correct?
So would I just take 17/60 and times it by 2*pi*24.5?

Thank you so much for taking time to help me with that. I was really getting hung up on where to start or if I needed an equation.

nccaitlin91 · Mar 27, 2013, 07:27 AM

Originally Posted by nccaitlin91

2pi*r correct?
So would I just take 17/60 and place that in the "r" of 2pi*r to get the radians per second?

Thank you so much for taking time to help me with that. I was really getting hung up on where to start or if I needed an equation.

1.8 times 24.5= 43.6 is the answer I got from that

ebaines · Mar 27, 2013, 07:38 AM

There are 2 pi radians in a circle, not 2 pi r. So to convert from rev/sec to radians/sec multiply by 2 pi radians/rev. Note how the units cancel out leaving the answer in terms of rev/sec.

nccaitlin91 · Mar 27, 2013, 07:44 AM

Originally Posted by ebaines

There are 2 pi radians in a circle, not 2 pi r. So to convert from rev/sec to radians/sec multiply by 2 pi radians/rev. Note how the units cancel out leaving the answer in terms of rev/sec.

So I should just stick to the 1.78rad/s ( which I rounded to 1.8 earlier) and not worry with the 24.5 at all?

ebaines · Mar 27, 2013, 07:49 AM

Yes, 1.78 rad/sec.