Reddit reviews SuperElastic Nitinol #1 (56% Nickel, 44% Titanium) Wire, Light Oxide, Straightened, 0.011" Diameter, 36" Length (Pack of 1)

I would use a nitinol (shape memory alloy) activator. you can easily build a rotating platform, and use a bit of nitinol wire attached to a pulley or lever to activate the mechanism.

you could make a spring like this... and just attach a battery and switch (here is simple spring activator using nitinol):

http://www.youtube.com/watch?v=0L2UEF-9bF4

nitinol wire is pretty cheap. about $1/foot, here you go:

http://www.amazon.com/SuperElastic-Nitinol-Titanium-Straightened-Diameter/dp/B000FMYBRQ

it would just be up to you to build a rotating platform using wood/plastic or lego mindstorm... or just some hard-board would probably do... you'll have to include some hard-stops to precisely stop your rotating platform. Of course, you would have to have two counteracting nitinol wires to 'return' the rotating stage to its original position, but that's easy. Nitinol is really strong, you could rotate a car if you had 10 feet of it and the right lever/pulley design.

Another suggestion is to get an old microwave with a rotating platform and tear it apart. disable the microwave generator (umm, obviously) and then just time how long it takes to rotate 180deg. simple, but less precise than the nitinol solution

good luck!