Nib asked, and Nib — askNib's tutor — drew the answer live at a whiteboard. This is the spoken transcript; enable JavaScript to watch it drawn.
why does a ball curve when it spins
A free kick can bend around a wall of defenders, ending in the goal. A ball kicked straight would just hit them. The only difference is spin.
Here is the rule. Seen from above, this ball turns clockwise, so its front edge turns to the right. The ball swerves toward the way its front edge is turning.
Why? Put the ball in the wind. Without spin, air splits around it evenly and leaves evenly, so nothing pushes it sideways. Here the air is blowing past a ball flying left.
Now spin it clockwise. The ball's top surface moves with the air and drags a layer of it along, so the air leaves the ball bent downward, behind it.
Newton's third law finishes it. The ball shoves the air down, so the air shoves the ball up. Spin turns passing air into a sideways push.
So the whole idea: spin drags the air one way, the ball is pushed the other, and it swerves toward where its front edge turns. That's how a kick curves round a wall.
A spinning ball drags air along, flings it aside, and gets pushed the opposite way: that's the curve.