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tangibleLime
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Rotation of a Fan - Unsolved
A ceiling fan with 85cm diameter blades is turning at 66 rpm. Suppose the fan coasts to a stop 26 s after being turned off.
What is the speed of the tip of a blade 10 sec after the fan is turned off?
[tex]\alpha=\frac{w_{2}-w_{1}}{\Delta t}[/tex]
[tex]v=r\omega[/tex]
First I converted 66 rpm to rad/sec, resulting in [tex]6.912[/tex] (http://www.wolframalpha.com/input/?i=66+rpm+to+rad/sec)
Then I found the angular acceleration using [tex]\alpha=\frac{w_{2}-w_{1}}{\Delta t}[/tex] as [tex]\alpha=\frac{0-6.912}{26}[/tex], which resulted in [tex]\alpha=-0.265846[/tex].
I then (this is where I think I have made a mistake) plugged this new alpha value back into that same equation to come up with this: [tex]-0.265846=\frac{w_{2}-6.912}{10}[/tex], since I figured I need [tex]\omega[/tex] to use in the [tex]v = r\omega[/tex] equation. That resulted in [tex]\omega=0.425[/tex]/
Now I used [tex]v = r\omega[/tex] as [tex]v = (.85)(0.425)[/tex], resulting in [tex]v = 0.36[/tex], which was determined to be incorrect. I'd start doing some trial and error, but the homework system cruelly deducts points for each incorrect answer.
I also tried the following, but it also failed. I used the equation of motion [tex]v=v_{0}+at[/tex] as [tex]\omega=r\omega_{0}+(\alpha * t)[/tex] with the values of [tex]\omega=0.36125 + (-0.265846)(10)[/tex], resulting in [tex]4.3[/tex]. This answer is incorrect.
Homework Statement
A ceiling fan with 85cm diameter blades is turning at 66 rpm. Suppose the fan coasts to a stop 26 s after being turned off.
What is the speed of the tip of a blade 10 sec after the fan is turned off?
Homework Equations
[tex]\alpha=\frac{w_{2}-w_{1}}{\Delta t}[/tex]
[tex]v=r\omega[/tex]
The Attempt at a Solution
First I converted 66 rpm to rad/sec, resulting in [tex]6.912[/tex] (http://www.wolframalpha.com/input/?i=66+rpm+to+rad/sec)
Then I found the angular acceleration using [tex]\alpha=\frac{w_{2}-w_{1}}{\Delta t}[/tex] as [tex]\alpha=\frac{0-6.912}{26}[/tex], which resulted in [tex]\alpha=-0.265846[/tex].
I then (this is where I think I have made a mistake) plugged this new alpha value back into that same equation to come up with this: [tex]-0.265846=\frac{w_{2}-6.912}{10}[/tex], since I figured I need [tex]\omega[/tex] to use in the [tex]v = r\omega[/tex] equation. That resulted in [tex]\omega=0.425[/tex]/
Now I used [tex]v = r\omega[/tex] as [tex]v = (.85)(0.425)[/tex], resulting in [tex]v = 0.36[/tex], which was determined to be incorrect. I'd start doing some trial and error, but the homework system cruelly deducts points for each incorrect answer.
I also tried the following, but it also failed. I used the equation of motion [tex]v=v_{0}+at[/tex] as [tex]\omega=r\omega_{0}+(\alpha * t)[/tex] with the values of [tex]\omega=0.36125 + (-0.265846)(10)[/tex], resulting in [tex]4.3[/tex]. This answer is incorrect.
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