- #1
PFuser1232
- 479
- 20
In chapter 1 of the book "Introduction to Mechanics" by Kleppner and Kolenkow, the derivative of a generic vector ##\vec{A}## is discussed in terms of decomposing an increment in ##\vec{A}##, ##Δ\vec{A}##, into two perpendicular vector vectors; one parallel to ##\vec{A}## and the other perpendicular to ##\vec{A}##
Two equations are then derived:
$$|\frac{d\vec{A}_{perp}}{dt}| = A\frac{dθ}{dt}$$
$$|\frac{d\vec{A}_{par}}{dt}| = \frac{dA}{dt}$$
Do these equations fail if ##θ## or ##A## decrease with time (since the magnitude of a vector is always positive or zero)?
Two equations are then derived:
$$|\frac{d\vec{A}_{perp}}{dt}| = A\frac{dθ}{dt}$$
$$|\frac{d\vec{A}_{par}}{dt}| = \frac{dA}{dt}$$
Do these equations fail if ##θ## or ##A## decrease with time (since the magnitude of a vector is always positive or zero)?