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Moment of Inertia and torque? 
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#1
Dec609, 04:22 PM

P: 62

1. The problem statement, all variables and given/known data
The combination of an applied force and a frictional force produces a constant total torque of 39.9Nm on a wheel rotating about a fixed axis. The applied force acts for 4.5s, during which time the angular speed of the wheel increases from 3 rad/s to 12 rad/s. The applied force is then removed. The wheel comes to rest in 72s. A. What is the moment of inertia of the wheel? Answer in units of kgm^2 B. What is the magnitude of the frictional torque? Answer in Nm C. What is the total number of revolutions of the wheel? 2. Relevant equations [tex]\sum[/tex][tex]\tau[/tex] = I(moment of inertia) * [tex]\alpha[/tex] 3. The attempt at a solution A. 39.9 = 2I I = 19.95 That is correct. B. T = (19.95)(9/72) = 2.49375 That is incorrect. What am I doing wrong? C. I need some help, do not know where to start. Thanks in advance. Sorry if the equations look bad. This the first time I am using Latex and I still don't know exactly how to use it correctly. 


#2
Dec609, 04:29 PM

P: 62

Well I just I figured out Part b. Instead of doing 123/72, I had to do 12/72. Can somebody explain that to me please.



#3
Dec609, 04:33 PM

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#4
Dec609, 04:34 PM

P: 62

Moment of Inertia and torque?
Oh right, thank you. Any help for part C? Just a way for me to get started please.



#5
Dec609, 04:37 PM

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First you need to find the total angle of rotation during the acceleration part and during the deceleration part (you must have seen the formula [itex] \theta = \omega_i t + 1/2 \alpha t^2[/itex]). Then add the two angles for the total angle and fivide by 2 Pi to get the number of revolutions 


#6
Dec609, 05:38 PM

P: 62

So could I do this: theta = (1/2)(12/72)(72^2) for the decelerating part and for the accelerating part could I use the other formula: 12^2  9^2 / 2(123/4.5). Then add those together and divide by 2pi?



#7
Dec609, 06:36 PM

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For the accelerating part, it sounds good except that you mant 3^2 instead of 9^2. 


#8
Dec609, 06:41 PM

P: 62

Yes I meant 3^2 instead of 9^2. But isn't omega_i zero because is it come to rest when it decelerates.



#9
Dec609, 07:04 PM

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