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The point on the bottom of a rolling object is instantaneously at rest. Acceleration? 
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#1
Feb2510, 02:24 PM

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1. The problem statement, all variables and given/known data
The point on the bottom of a rolling object is instantaneously at rest (v = 0). What is the acceleration of that point? 2. Relevant equations 3. The attempt at a solution The formula given is a = [tex]\alpha[/tex]r, and r = 0. So I'm guessing it's zero as well, although that doesn't seem to make logical sense. Can anyone confirm that the answer is indeed zero? (By the way, the equation for v = [tex]\omega[/tex]r, and in this case r = 0. So r has to be zero for the equation for a as well. 


#2
Feb2510, 02:30 PM

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Confirmed instantaneously, zero. The entire wheel accelerates instantaneously relative to the point of contact. The point of contact is the only point on the wheel that is at rest with respect to an inertial frame, namely the floor.



#3
Feb2510, 02:36 PM

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Just because the point of contact is instantaneously at rest does not mean its acceleration is zero.



#4
Feb2510, 02:52 PM

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The point on the bottom of a rolling object is instantaneously at rest. Acceleration?
Seems like I'm getting conflicting answers...
If that's wrong, then how does the formula a = αr work in this case? I know in general that formula is useful for "converting" angular acceleration to linear acceleration, but how does it pertain to the bottom of a rolling object? 


#5
Feb2510, 03:06 PM

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To find the acceleration of a point on the rim, consider the motion of that point with respect to the center of mass. 


#6
Feb2510, 03:13 PM

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Why the center of mass? Isn't the axis in this case the bottom of the wheel?



#7
Feb2510, 03:31 PM

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And you didn't answer my question: What's the angular acceleration of this rolling object? 


#8
Feb2510, 06:37 PM

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#9
Feb2510, 06:45 PM

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(2) The acceleration is the same in any inertial frame, including the one in which the center of mass is at rest. Of course, from the center of mass frame it is easy to see that that point of contact is accelerating. 


#10
Feb2510, 07:46 PM

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