can some one give me the concept of arc and curvature( related to calculus 3)

Question

anonymous · Answer

curvature is the rate where the unit vector T turns  per unit of length. it is calculated $$k=|dT/ds|$$

anonymous · Answer

if you are given a position, you can find T by dividing the derivative of position over the absolute value of it. it can be looked at as velocity over speed$$r'(t)/|r'(t)|$$

anonymous · Answer

ds refers to arc length parameter for a curve. if you're given a curve r(t)=x(t)i+y(t)j+z(t)k, $$s(t)= \int\limits_{t _{0}}^{t} (dx/dt)^{2}+(dy/dt)^{2}+(dz/dt)^{2} dt$$

anonymous · Answer

now, k can be re written as $$k=|(dT/dt)(dt/ds)|$$

anonymous · Answer

hmm.........ok thanx

anonymous · Answer

elica?

anonymous · Answer

the purpose of finding an arc length can be thought of as wanting to know how sharp a curve is turning

anonymous · Answer

i just finished this class so my explanation might not be detailed enough since i need to understand more but i shared what i can

anonymous · Answer

in which class u r?

anonymous · Answer

calc III just had the finals on monday