AboutAlon Mandes Expertise Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems.
Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience 1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Question I want to know the thread lenght if it is wound on a cylinder at a certain pitch.
eg. cylinder 50mm dia.
pitch 12mm
consider the thread is wound for 10 times(i.e 10 pitches)
Thanks
Answer Let's make parametrization to our thread Lulianic curve :
x(t)=25cos(t)
y(t)=25sin(t)
z(t)=12t , 0<t<2pi .. r(t)=[x(t),y(t),z(t)]
Length of the curve is Integral(t from 0 to 10pi) of |r'(t)| dt
Now, x'(t)=-25sin(t) , y'(t)=25cos(t), z'(t)=12.
All you have to do now is to calculate the integral.
