## Fictious force: Cylinder on an Accelerating Plank

1. The problem statement, all variables and given/known data

Problem is described in the picture

I do not understand how can $\alpha^{'}R=a^{'}$.
The dimensions do not seem correct. Angular velocity x distance from the origin = tangential velocity, is that correct ? How can this equal acceleration then ?

3. Attempt to solution

I think that $\alpha^{'}R=a^{'}$ would hold only if we would consider a unit time. That is:
$\alpha^{'}R=\frac{d\theta}{dt}R$, which, more by knowing the anticipated result in this case, than by logic, gives $\frac{d\theta}R = a^{'}dt$ which is now dimensionally OK, I think...
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 Quote by Leb I do not understand how can $\alpha^{'}R=a^{'}$. The dimensions do not seem correct. Angular velocity x distance from the origin = tangential velocity, is that correct ? How can this equal acceleration then ?.