James R

What are the equations which relate the quantities in each of your questions? Let me do the first one for you. An object of mass m in circular motion of radius r at constant speed v has a centripetal force on it, given by: F = mv^2/r It's acceleration is: a = F/m = v^2/r The relationship between the force and acceleration is F = ma. So, the graph of F against a will be a straight line through the origin with slope m. Does that help? Now try the other two questions and tell me what you think.

When people say things like "the universe is spherical", they aren't usually referring to the usual 3-dimensional sphere. More probably, they're referring to a particular 4-dimensional model of our universe's spacetime. A good analogy is to drop one dimension. Imagine that you can only travel on the surface of the Earth: north, south, east or west, but you have no knowledge of "up and down". The geometry of the Earth's surface is the geometry of a sphere (obviously) in 3 dimensions, but you live in 2 dimensions. Where is the "centre" of the sphere? It's at the centre of the Earth. But, as a 2-dimensional being, you can't point to it, since it exists in the "down" direction, and you don't know about "down". In fact, from your 2-dimensional perspective, where the SURFACE of the Earth is all that exists, your world has no centre. If you move off in one direction, you eventually end up back where you started. And no point on the Earth's surface is "more special" than any other point, so no point on the surface can be considered to be the "centre". Now go to our actual universe. Suppose we live on the 3-D surface of a 4-sphere. We only know about the directions north, south, east, west, up, down. We can't point in the direction of the centre of the 4-sphere, and in fact the centre is not part of the space we inhabit. Our universe therefore has no centre in the usual sense.