Insulated conductor is a conductor that is not connected by another conductor to anything else.
Any time there is a potential difference between two conductors there are excess charges. When you connect the two together, charges flow from one to the other until the potential difference is zero.
No, your instincts are correct, you friend's are not. If you fire a BB too fast, the air resistance will melt it. But that would be a lot faster than 1800fps.
And, Botemp, the air friction is proportional to the _square_ of velocity.
Simplest demo is to take a pendulum. With no sideways velocity, it passes through centre. This is equivalent to moon hitting the earth. If it has just the right sideways speed, it will travel in a circle with this sideways speed continually. That's analogous to what the moon is actually doing...
The y is a dummy variable; it is integrated out. If you want insight into the solution, try some other easily integrable cases. For example, what if u_0 is a delta function? Or try plotting the integrand for a sequence of different y's, then imagine them all added together.
Pressure, density (n/V), and temperature are 3 quantities related by the gas law. If you change one of them, you don't know how the other two change; you need more information. So for example, if you slowly compress a gas that's in contact with a heat reservoir, then T=constant and so PV =...
Watch out for words like "merely" in textbooks.
It's not sensible to say that magnetic fields are merely the result of electric fields plus relativity. One could as well say that electric fields are magnetic fields modified by relativistic effects. It is more accurate and less confusing to say...
Try this thought experiment. Empty the universe of all mass except yourself. Say you have a method like rockets or something to make yourself spin. How would you know you are spinning? If you are not spinning against anything else, could you be said to be spinning? Mach concluded not only that...
|x+1| is always >0. Now look at the right side. It means that x MUST be larger than 1/2. So x+1 is >0 and we drop the absolute value sign: x+1=2x-1. It's pretty easy to solve.