Why is the Instantaneous Speed Zero in this Rotational Motion Problem?

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In the discussed rotational motion problem, the instantaneous speed at the point of contact between a rolling object and the surface is zero due to the condition of rolling without slipping. This means that the point of contact does not move forward or backward relative to the surface. The instantaneous speed is determined by the combination of translational and rotational speeds, which are equal in magnitude but opposite in direction at that point. The lack of sufficient data prevents calculating the specific rotational speed, but the key takeaway is that the net speed at the contact point is zero. Understanding this concept is crucial for analyzing rolling motion dynamics.
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Homework Statement


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Homework Equations



##v = r \omega ##??

The Attempt at a Solution


The answer is 0...why?
 
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Because the "object is rolling without slipping". That means that any point on the objects circumfence that is in contact with the surface on which it is rolling does not move forward of backward on the surface.

(Oh, and saying "the instantaneous speed is 0" is NOT the same as saying "there is no instantaneous speed"!)
 
The speed of any point of the rolling body is the sum of its speed due to translational motion and its speed due to rotational motion.

What is the translational speed of the point of contact of the rolling body?

What is the rotational speed of the point of contact of the rolling body?
 
Well, I now see that there isn't enough data in the problem to calculate the rotational speed of the point of contact. But, the key idea is that the translational speed and the rotational speed are equal and opposite, leading to a net force of zero.
 

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