Kinetic Energy and Centripetal Force I know since no work is done by the centripetal force, kinetic energy is constant; but does that mean it if the kinetic energy was increased or decreased it would have no effect on the centripetal force? 
 A: It would have no effect on the force, which in general has a separate cause and does not depend on speed or alike (it may depend on gravity or friction or alike depending on the situation). 
The centripetal force is:
$$F_c=m\frac{v^2} r$$
Decreasing the kinetic energy $K=\frac12 mv^2$ of the circulating object means decreasing either $m$ or $v$. Doing either would mathematically seem to decrease $F_c$ (one linearly and the other quadratically). But we know that doesn't happen. What happens instead is that $r$ changes accordingly.
The conclusion is that a change in the kinetic energy of a circulating object changes its orbit, but not the centripetal force pulling in it.
As per comment, let me cover the situation of a fixed orbit as well. If you imagine a fixed distance of the circulation, for example when swinging a ball in a string around or when turning in a curve and always adjusting your wheels in order to keep the same radius while speeding up, then even when having higher speed, the distance is fixes. This will according to the formula above change the force. 
OBS OBS is may happen that the force changes anyways for changed speed because it depends on that changed distance. For example with gravity when i.e. the moon orbits Earth, the centripetal force actually does depend in distance and thus on the orbit. In such cases changing the kinetic energy may indirectly change the force. 
A: Depends.
If your going around a curve of radius R. Then increasing the kinetic energy implies increasing the velocity and hence now you need some more centripetal force to maintain the same radius.  
Now if your going around a circle with increasing velocity, and the radius of the path your going around also increases. Only $\frac{mv^2}{R} = $ centripetal force, 
needs to evaluate the same.
A: If kinetic energy was increased or decreased, there would, in most of the cases be a change in the centripetal force.
"If kinetic energy was increased or decreased" implies that speed (you may also use the term instantaneous tangential velocity) has increased or decreased (assuming mass is unchanged).
Under these circumstances, the centripetal force required to keep the same path of motion - ie, the same radius, would indeed be more.
An example of this would be:
Suppose a string has a toy car tied to one end, and the other  end is fixed to a nail hammered on to a smoth table. If the car is switched on, it rotates about the nail as the center, and the nail will eexperience a tug, and the nail will have to provide, through the tension in the string, a centripetal force to keep the toy car in its fixed circular path. 
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If the toy car is speeded up, the nail and string will have to provide a greater magnitude of centripetal force to keep the same radius.
(this can be verified by inserting a small spring balace in the string)
No change in centripetal force despite a change in kinetic energy (change in speed with mass constant) is possible only if there is a change in radius ie, the string becomes longer or shorter.
Perhaps you wish to ask - if centripetal force is not doing work, then how come there is an increase in kinetic energy?
The source of this kinetic energy lies elsewhere - in the above example, the car speeding up is possible if its batteries provide more power.
