Ideas for making center of gravity toys?--physics project?

Answer 1

How about a seesaw?
It could have a movable pivot point, and you could put various things on the ends, and show that when you either change the mass of the objects on one end, the pivot point must change, or that when you change the POSITION of one of the masses (closer to or farther from the end) the pivot point changes.
The pivot point is the center of gravity.

Answer 2

This is a cool one that you can find in most science centers:

a double cone moves up an set of inclined rails its centre of gravity lowers. The double cone appears to roll uphill. A double cone rolls up an inclined track. Make a circular cone with two heads: (a) Tape together two plastic funnels at their mouths with a smooth connection. (b) Cut out two identical equilateral triangles from cardboard with one side in the shape of an arc. Roll the triangles, beginning at a straight side, then tape together the straight sides to form two circular cones. Rub smooth the bottom of each cone and tape them together.
(ii) Make a ramp: (a) Cut out a long narrow strip of cardboard and fold in half to make a V-shape. Cut cardboard in rectangle shape and tape it to the V-shape to make a ramp. (b) Use two rulers leaning on a book or use two drinking straws.
(iii) Put the cones on a lower end of the cardboard ramp. If the surfaces of the cone and ramp are smooth the cone rolls up along the ramp.
(iv) Adjust the upper distance between two rulers or straws to make the cone roll up or down the ramp. Hold the upper ends of the rulers or straws to first make the distance between them small then move them apart until the cone begins to roll upward. Before the cone arrives at the top of the ramp decrease the distance between the two ends of the rulers or straws to make the cone roll down. Measure the height of the top of the cone before and after the rolling. The top of the cone after rolling is lower than the height before the rolling. The cone is symmetrical so its centre of gravity is on the line the connecting of the two tops, so the height of the tops is the height of the centre of gravity of the cone. When the bottom of the ramp is narrower, the cone at the lower place of the ramp has a higher centre of gravity. While the cone rolls up to the top of the ramp due to the wider width of the top, the centre of gravity of the cone is lower. Thus the centre of gravity of the cone is higher at bottom, the centre of gravity of the cone is lower at the top, so the cone does not roll upward but downward.
(v) An object in the shape of a cylinder cannot roll up itself on such a ramp, because its centre of gravity will rise.
(vi) Repeat the experiment with a ball. Put a ball with a suitable size on the ramp. It can roll up itself and the speed of rolling is faster than the speed of a cone.

Answer 3

Mobiles, like what you hang in front of babies, are great examples of 2-D center of mass problems.

Answer 4

A spinning top