# Velocity of an stationary object when viewed from rotating disk

Suppose I am sitting at the centre of a rotating disk, having an angular speed of 3 radian per second and I observe a tree 4 meters away from me. The tree will have a velocity of 12 meters per second in my frame with a direction opposite to my sense of rotation.

Now if I sit on the edge of the rotating disk then I read that the velocity of the tree will be exactly the same in my frame again.

Can you please explain this to me without math or simple math because I am not able to visualize how this will be?

In your frame of reference (in both situations) you are at rest and the tree is rotating with 3 radian per second 4 meters away from the center. It does not matter whether you sit at the center or on the edge of the rotating disk, i.e. where in your frame you are at rest. The relative motion between the frames is the same in both cases.

Without any sums other than those you have produced imagine the disc being of a radius $$4$$ metres, the same distance as the tree is from the centre of the disc, with the centre of the disc not moving relative to the ground.

The edge of the disc is moving at a speed of $$12 \,\rm m/s$$ relative to the ground/tree. If you stand on the edge of the disc you are not moving relative to the disc.

So wherever you stand on the edge of the disc your speed relative to the tree will always be $$12 \,\rm m/s$$ relative to the ground/tree and only the direction of the relative velocity between edge of disc/you and ground/tree will change.

I now rewrite the last sentence as the general case.

So wherever you stand on [xxx xxxx xx] the disc your speed relative to the tree will always be $$12 \,\rm m/s$$ relative to the ground/tree and only the direction of the relative velocity between edge of disc/you and ground/tree will change.

This is because you are not moving relative to the disc and so the edge of the disc is not moving relative to you.

I suspect that you question was asked because you surmised that as you moved closer to the tree the distance between yourself and the tree decreased and so did the relative velocity between yourself and the tree.
What you missed is that whilst you are on the disc other than at its centre you are moving relative to the ground and so must add that motion when evaluating the relative velocity between you and the tree.
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