|MadSci Network: Astronomy|
Thanks for an interesting question. You've got the pieces needed for the answer already: you know that it takes 8 minutes for light to get from the Sun to the Earth, and that the Sun's apparent daily motion in the sky is due to the Earth's rotation. [Of course, the Sun also appears to move against the background stars as the Earth orbits it, but we can ignore that here.]
Ok, so the Earth stops rotating at time t=0. The light we see from the Sun at that time was emitted at time t=-8, and the Sun is a certain distance above the horizon. Now consider time t=8. The light we see then was emitted at time t=0, and the Sun is still in the same position relatvie to the horizon because the Earth has stopped rotating. So there is no 8-minute lag in the Sun's apparent motion: it appears to stop right when the Earth does. I found it helpful to draw a diagram to see this clearly; this might be useful for your class presentation as well.
Here's another way to think about this. The stars also appear to rise and set because of the Earth's rotation, but of course they are much further away. The light from the nearest stars takes about 4 years to get here. But if the Earth stopped rotating, it doesn't make sense that it would take >4 years for the stars to stop rising and setting (or that it would take longer for more distant stars to stop!) So the effect we are imagining here is a local one, due to things happening on the Earth.
This MadSci answer has some more details on "stopping the Earth", and if you search our archives you'll find some computations of how much energy this would actually take.
Try the links in the MadSci Library for more information on Astronomy.