Alternatively, and to get back to the question of cyclones etc., consider the model where the golfer is on the edge of the merry-go-round and the observer is on the fixed chair/platform.
With the merry-go-round stationary, the golfer hits the ball; it goes straight along one of the radial lines (and over a fixed line on the ground) into the cup. Suppose the observer, and the golfer at that point, are at the south edge of the merry-go-round.
With the merry-go-round going anti clockwise (a model of the earth's west to east rotation viewed from above the North Pole), if the golfer hits the ball from the south edge and it goes into the cup, it still travels in a straight line as viewed from an external frame of reference (the observer sees it go over a fixed line on the ground). To do this, the golfer would have to incorporate into his swing a backward component - to him, the ball would appear not follow a radial line on the moving merry-go-round, but the spiral path mentioned above.
Alternatively, if the golfer just hit the ball along the northwards radial line, it would miss the cup and go past it on the right. The northward hit of the golfer, combined with the eastward motion of the edge of the merry-go-round, would take it on a route seen by the observer to go through a vertical plane angled north-eastwards, not directly north. Similarly, a parcel of air at the equator in a high pressure region, trying to fill a depression to its north, is impelled by the pressure gradient to go north plus a component to the east provided by the earth's rotation, so it misses the centre of the depression and passes it to the right.
Meanwhile, one can follow a similar analogy for a golfer at the centre hitting a ball to the edge, and a parcel of air at the North Pole trying to fill a depression to its south. It will miss and pass by on the right side as viewed by the golfer/from the North Pole - i.e. to its west.
So air trying to reach a depression in the northern hemisphere goes up the eastern side and down the western side, imparting anticlockwise rotation to a cyclone/low pressure. Air going towards it from other points of the compass is similarly deflected to varying degrees, which happen to work to give an entirely circular motion. Viewed from outside the earth (the observer outside the merry-go-round), there is no real acceleration in any direction except the initial impetus. But viewed by somebody rotating with the merry-go-round/earth, the ball/air seems to acquire an acceleration making go in a spiral - the coriolis acceleration. That is why it is an apparent, not real, acceleration.
Hope that helps.
Chris N.