## From linear to angular

Let’s consider the body C, rotating around the point O. The linear speed of point A is given by .

The angular velocity around O is given by :

## From angular to linear

Assuming the angular velocity is known, the linear speed at point A is given by:

## Example

```
close all;
clear all;
clc;
%% Parameters
% Coordinates of point O
O=[0;0;0];
% Coordinates of point A
A=[1;2;0];
% Coordinates of point B
B=[2;1;0];
% Speed applied at point A
VA=[0;2;0];
%% Compute angular velocity
% Compute vector OA
vOA=A-O;
% Compute angular speed around point A
wO=cross (vOA,VA)/(norm(vOA)*norm(vOA));
%% Compute linear speed at point B
vOB=B-O;
VB=cross(wO,vOB);
%% Draw system
plot3(O(1),O(2),O(3));
hold on;
line ([O(1) A(1)],[O(2) A(2)],[O(3) A(3)]);
line ([O(1) B(1)],[O(2) B(2)],[O(3) B(3)]);
text(O(1)+0.2,O(2)+0.2,O(3)+0.2,'O','FontSize',100);
text(A(1)+0.2,A(2)+0.2,A(3)+0.2,'A','FontSize',100);
text(B(1)+0.2,B(2)+0.2,B(3)+0.2,'B','FontSize',100);
% Draw speed at point A
hFA=quiver3 (A(1),A(2),A(3),VA(1),VA(2),VA(3),'Color','k','LineWidth',3,'MaxHeadSize',1.5);
% Draw speed at point O
hTO=quiver3 (O(1),O(2),O(3),wO(1),wO(2),wO(3),'Color','g','LineWidth',3,'MaxHeadSize',1.5);
% Draw speed at point B
hFB=quiver3 (B(1),B(2),B(3),VB(1),VB(2),VB(3),'Color','r','LineWidth',3,'MaxHeadSize',1.5);
% Display axis and legends
grid on;
axis square equal;
xlabel('X');
ylabel('Y');
zlabel('Z');
legend ([hFA,hTO,hFB],'Linear speed at point A','Angular velocity a point O','Linear speed at point B');
```