[dellagd]

Originally Posted by Ether

What formula did you use to calculate the above? Show your work please.

Its a system of 4 equations, I just solved for Vcy and and then got Vcx from the ratio of Vcy/Vcx.

Spoiler for Solving:

2 + Vcy = Fy
Vcx = Fx
Fy/Fx = -(28/12) / 2 #Known angle of vector sum/friction
Vcx/Vcy = (28/12) / 2 #Known angle of carpet velocity

Substitute in for Vcx and Fx:

2 + Vcy = Fy
((28/12)/2) * Vcy = (-2/(28/12)) * Fy

Substitute in for Fy:

2 + Vcy = ((-(28/12)^2)/(2^2)) * Vcy
Vcy = -.847

Into another equation:

Vcx/(-.847) = (28/12)/2
Vcx = -.988

Robot Velocity components are opposite of these.

Vry = .847
Vrx = .988

Vr = sqrt(.847^2 + .988^2) = 1.302 ft/s

Vtangential = r * omega

r = d/2 = sqrt(2^2 + (28/12)^2)/2 = 1.537 ft

omega = Vt / r = 1.302 / 1.537 = .847 rad/s

Originally Posted by Ether

Does that value of omega agree with your Vcy and Vcx calculations above??

Yes, via the equation Vt = r * omega