Remaining in the same spot on a spinning disk

[Fibo112]

I am still bothered by this questions notion of acceleration, it just doesn't make any sense to me to be talking about acceleration without a clear frame of reference as to where this acceleration is taking place...

 

[haruspex]

I am still bothered by this questions notion of acceleration, it just doesn't make any sense to me to be talking about acceleration without a clear frame of reference as to where this acceleration is taking place...

The question states that the child is to stay in the same place in the laboratory frame. That is enough to determine the force the child must exert on the disc, and the disc's consequent acceleration.
The slightly awkward part is that it asks for "the child's acceleration relative to the disk." I now consider that ambiguous. I think what they want is relative to the tangential acceleration of the disc. But if it means relative to the reference frame of the rotating disc then you would have to add the apparent radial acceleration, $-\omega^2\frac R2\hat r$.

 

[Fibo112]

Ok. Thanks a lot for your help.