Velocity Back to Polar
To convert velocity back to polar:
vx = -w r sin(q) vy = w r cos(q)
v = [vx2 + vy2]1/2 = [w2r2 sin2(q) + w2r2 cos2(q)]1/2
= wr[sin2(q) + cos2(q)]1/2 = wr
qv = inv tan[vy/vx] = inv tan[wr cos(q) / -wr sin(q)]
if wɬ, +cos(q)=+sin(q+90o); -sin(q) =+cos(q+90o)
if wɘ, -cos(q)=+sin(q-90o); +sin(q) =+cos(q-90o)
qv = q ?90o . Note that the direction of the velocity, qv, is perpendicular to the direction of the position (the radius), which means the velocity is tangent to the circle.