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xdem713o

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Sep 2, 2009
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My homework question is "determine the angular velocity in radians per second of a wheel that completes 50 revolutions per minute." I have similar homework questions to this and have been pulling my hair out for about 3 hours now. I need help!!
 


Gosh, this is fairly basic. I'm wondering why you're stuck because you made no statements about what you've tried or what you're thinking. (What did you do, for those 3 hours?)

Do you know what a central angle is?

Do you understand radian measure for angles?

As a wheel turns, the central angle grows.

Angular velocity is the rate at which the central angle grows. (It's usually stated as some number of radians per some unit of time.)

Each complete revolution of the wheel causes the central angle to grow by 2*Pi radians.

Therefore, if a wheel rotates once per minute, then the angular velocity is 2*Pi radians/minute.

If a wheel rotates twice per minute, then the angular velocity is 4*Pi radians/minute.

If a wheel rotates three times per minute, then the angular velocity is 6*Pi radians/minute.

If a wheel rotates four times per minute, then the angular velocity is 8*Pi radians/minute.

If a wheel rotates 10 times per minute, then the angular velocity is 20*Pi radians/minute.

In other words, if we're told a specific number of revolutions in one minute, then we need to find by how many radians the central angle grows in that minute. As shown above, we simply multiply the number of revolutions by 2*Pi.

The second part of this exercise involves a unit conversion. You need to convert radians per minute to radians per second. This conversion works the same way as converting linear speed.

Do you know how to convert something like 100 feet/min to the corresponding velocity in feet/sec ?

I really have no idea where you're at. Are you able to ask any specific questions ?

 
Sorry about that.. I've tried to work that out. I realized that if you multiply the number of revolutions by 2 pi because one revolution is 2pi. So I would multiply 50 by 2pi. But our professor has urged us to look at the back to make sure our answer matches the answer with the back and the answer says 5pi/3 rad/sec. This is what confused me. After I multiplied 50 revolutions by 2pi I got 314.16. This is where I got stuck.
 
mmm4444bot said:
… The second part of this exercise involves a unit conversion. You need to convert radians per minute to radians per second. This conversion works the same way as converting linear speed.

Do you know how to convert something like 100 feet/min to the corresponding velocity in feet/sec ? …
 
I understand that I need to convert the rad/minute to rad/sec but I'm not quite sure what conversions I need (60 sec/1 minute). And I'm getting decimals answers when I need answers such as pi/50 or 3pi/5.
 
xdem713o said:
… I multiplied 50 revolutions by 2pi I got 314.16 …


Don't substitute a decimal approximation for Pi. In other words, work with exact values.

100 Pi radians/minute

 
So I end up with 100pi after multiplying 50 revolutions by 2pi. I would think that I need to convert that to seconds by multiplying 60 sec/ 1 minute by this 100 pi. but I dont get 5pi/3
 
xdem713o said:
… I need (60 sec/1 minute) …


60 sec/1 minute is the conversion factor for converting from seconds to minutes.

Use the reciprocal, instead. We want the denominator units "minutes" to cancel. So, in the conversion factor, we need "minutes" in the numerator.

(100 Pi radians/minute)*(1 minute/60 seconds)

 
wow.. that wasn't so bad at all!! I was making it worse than it was. Thanks so much. Do you mind if I ask another question regarding angular velocity?
 
xdem713o said:
… Do you mind if I ask another question regarding angular velocity?


Of course not!

Please submit new exercises under a new thread. It helps, too, if you can ask specific questions, or show what you're thinking. 8-)

 
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