Controlled vs. Uncontrolled.
This is usually defined by the neutron generation rate. It would be wrong to define it in terms of the number of fissions because each fission releases 2.5 (on average) neutrons, and you have to absorb 1.5 neutrons. For controlled chain-reaction, the neutron generation rate must be exactly 1. This level of stability is actually incredibly difficult to achieve with just one source of prompt neutrons, a bit like trying to balance on the head of a pin. In practice, a power reactor is run at sub-critical, i.e. a prompt neutron generation rate less than 1, and the balance of the neutrons to reach 1.0 is made up of delayed neutrons that come from radioactive daughter products (this goes way beyond the syllabus). So a uranium power reactor is actually run at a sub-critical neutron generation rate by the use of control rods, and then the delayed neutrons top up the neutron flux to get to exactly 1.0 generation rate. Thank goodness for delayed neutrons, because without them, controlling the power output of a uranium-fuelled power reactor would be a nightmare.
Equal and opposite gravitational attraction.
Yes, this is certainly possible. Try to imagine modelling a gravitational field as being a bit like a topographic map of hills and valleys. Hills represent regions of high gravitational potential energy (GPE), and valleys represent areas of low GPE. The angle of the slope represents the strength of the local gravitational field. A free-falling object will roll down into a valley, or spiral into a depression. Any contour line across a topographic map that has the same elevation represents an equipotential path in a gravitational field, i.e. following that path does not require any change of GPE. Now imagine in our landscape of hills and valleys, there are two straight valleys, and they must be separated by a straight ridge. If you can stick to the ridge, you are traversing two gravitational valleys on either side. However, this is intrinsically unstable because you could fall to the left or the right at any moment, and you would fall into the strong gravitational attraction of one of the valleys. (If you are motivated, go look up Lagrange Points)
What do we mean by precision?
A working definition of precision is, how many significant figures can you quote in the result? The more significant figures, the more precise is the result. For example, a moving-coil voltmeter has a precision of 1% of the full scale reading, so 2 significant figures. A digital voltmeter with four digits has a precision of +/- 1 last digit, so that is 4 significant figures. However, you can have a very precise result, but it can also be inaccurate. Clearly, what we want is both a precise result AND an accurate result.
Back EMF graphs?
Yes, those graphs don't make sense, unless you realise they are averaging the amplitude of the back-EMF around one rotation of the armature. The average amplitude of the back-EMF is proportional to motor speed. If you hooked up a high speed oscilloscope to the motor, you would be able to see the fluctuations in the back-EMF around one rotation, and you would see it has a synchronous character.
