We got our Calc 3 tests today and as we were being shown how to get the answers, we came across a problem the teacher said "I'm curious that so many people got this question, maybe they learned it in some other class." I present to you the problem:
Recall that the angular momentum of a particle of mass
m along a path
R(
t) is defined by the vector quantity
L(
t) =
mR(
t) x
v(t). Consider a point
R(
t0) =
p on the planar curve
R(
t). Call
p a
point of maximal angular momentum if it has the property that amongst all particles of unit mass and unit speed on curves passing through
p, |
L(
t0)| is maximum. Suppose that each point of
R(
t) is a point of maximal angular momentum. What can we say about
R(
t)? That is, what kind of path does
R(
t) have to be?
Needless to say I got the question quite wrong....