[d/dt] |r| = 0 and |dr/dt| =/= 0

Explain what this says about the vector r (I may have switched the two equations, the second might actually be equal to 0 but I forgot what the question said now since it's been a while. And I'm sure that someone who knows about this will know which is which anyway)

Question

[d/dt] |r| = 0   and   |dr/dt| =/= 0

Explain what this says about the vector r (I may have switched the two equations, the second might actually be equal to 0 but I forgot what the question said now since it's been a while. And I'm sure that someone who knows about this will know which is which anyway)

anonymous · Answer

the first says that r is constant.  your second one doesn't make sense

anonymous · Answer

What if it was written the other way? [d/dt] |r| =/=0   and   |dr/dt| = 0

anonymous · Answer

sorry, is one supposed to be equal and the other not equal?

anonymous · Answer

Yeah

anonymous · Answer

I'm really sorry for not knowing which it is, just explain whichever case makes more sense

anonymous · Answer

the first says that the length of the vector is not changing becuase |r| is the magnitude (length) of the vector

$$\frac{ d }{ dt }\left| r \right|=0$$

the second says that the vector is changing, which means it's changing in some way.

$$\frac{ dr }{ dt }\neq0$$

so the vector must only be changing direction.

anonymous · Answer

make sense?

anonymous · Answer

Oh okay, so if I plotted every possible r vector, would I get a circle?

anonymous · Answer

think of the second hand of a clock.  the length of the hand isn't changing but it's always changing which direction it points (if its wound).

anonymous · Answer

and of course you'd get a circle

anonymous · Answer

Thanks! Makes much more sense now!

anonymous · Answer

you're welcome!