Please help me understand the use of dot operator

Hello. I have been having this same problem in a lot of the homework assignments I have been given so far.

What I am trying to do is use the while loop to create values for J, and in the same loop I am trying to use those values of

J to create a new array with the values from tau.

clc; clear ; clear all
F = 10; %Newtons
T = F*0.1 ;  %Work 
r = 0:5; %mm
i = 1


while i < 6
    
J = (.5*pi)*r.^4 

tau(i) = (T*r)/J

i = i + 1;

end

[KSSV]

Okay..what is the question now?

[Tsansoterra]

How do I get the values of tau using the values of J and r ? The method for J where I used a dot operator does not work for tau to cycle through the values of the array.

Answer 1

[Star Strider]

The dot operator, used with multiplication, division, and exponentiation, creates element-wise oiperations. See Array vs. Matrix Operations for a full explanation.

The one exception to that is the use of the dot operator in creating matrix transposes. The ‘regular’ matrix transpose (') creates the complex-conjugate transpose of a complex vector or matrix. Using the (.') creates the transpose without doing the complex-conjugate operation.

[Star Strider]

To calculate ‘tau’ without any loop (a loop is not necessary in this instance):

tau = (T*r)./J

The dot operator is necessary for the division, since ‘r’ and ‘J’ are vectors.

Note that ‘J’ was calculated correctly, using element-wise exponentiation.

[Tsansoterra]

Thank you. That was very insightful, and It gave me the asnwer I was looking for.

[Star Strider]

As always, my pleasure!

I do my best to provide complete explanations!

Answer 2

[David Hill]

Not sure what you want tau to be. Currently you have an array (T*r) divided by another array (J). If you want to generate a tau matrix, then:

tau(i,:)=(T*r)./J;

If tau is suppose to be a 6 element array, then I suppect what you meant was:

F = 10; %Newtons
T = F*0.1 ;  %Work 
r = 0:5; %mm
J = (.5*pi)*r.^4; 
tau = (T*r)./J;%need ./for element-wise operations

[Tsansoterra]

Hi David. Thank you for your response. I apologize for my laymen terms as this language is very new to me.

I have 3 equations ; T=F(0.1) , J=(pi/2)*r^4 , and tau = (T*r)/J

given ; r = 0:5 , T = 100, tau(max) = 100

I ultimately need to graph tau by r.

Using a while loop I am trying to get an array of answers for tau, so that I can graph it. Tau depends on the value J.

So what I want to do is run a while loop 5 times to represent each value of r. In this loop I am trying to solve for J, and then solve for tau using the found values of J.

Thanks again for your time.