(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A wheel of radius b rolls along the ground with constant forward acceleration a0. Show that at any given instant, the magnitude of the acceleration of any point on the wheel is

(a0^2 + (v^4 / b^2))^(1/2)

relative to the center of the wheel.

Here v is the instantaneous forward speed.

(I left out part of the question because I think I could get it after I get started on this.)

2. Relevant equations

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3. The attempt at a solution

I'm having difficulty getting this problem started really. I can go through my thought process on this problem. By looking at what they wish for me to solve, it seems those two accelerations are perpendicular to each other (a0 and v^2 / b). I think that v^2 / b is the centripetal acceleration actually, so this implies that a0 is actually the tangential component of the acceleration.

However, that is more of backwards reasoning in order to get the acceleration they want. I do not know why a0 would be the tangential component without knowing the answer in advanced. (Maybe I should? I don't think I've done a rotating wheel problem with acceleration in it before.) It's been a while since I've taken Physics 1 xD...

I tried to write down the position vector relative to the wheel, but I do not think I wrote it down correctly. I would think it would be of the form:

r(t) = bsin(wt)i + bcos(wt)j

But I realize w is not a constant here... So I'm not entirely sure.

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# Analytical Mechanics - rolling wheel (accelerating)

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