# Question about relative angular velocity

So i cant solve the first question
plz help me

tiny-tim
Homework Helper
welcome to pf!

hi svqweasdzxc! welcome to pf!
relative angular velocity of A relative to B is dθ/dt, where r and θ are the position of A, measured in a polar coordinate system whose origin is at B

(or, more realistically, it's the angular speed with which the kuiper belt object moves across the background stars! )

but i still dont know how to solve this problem,sorry.
plz forget my stupidity

Hi,
try to move the problem from angular speed to "linear" speed. The Earth moves with speed Ve, the KBO with speed V, so the relative speed between Earth and KBO is Ve - V.

Now, the "linear" speed can be rewritten as the angular speed times the radius, so we can write the relative speed as the distance between Earth and KBO multiplied by the relative angular speed (Vrel=Ve-V = ω(r-1)[AU]). Here your resoult.

(Note that this is true only in the case opposition or if r>>1)

I apologize for (really) possible English mistakes, I need a bit of training about that.

This relative business is always difficult. Think of the hands of an analog watch. Both are moving. The hour hand slower than the minute hand. If someone (very small) was to sit on the minute hand it would seem to him that the hour hand is rotating anticlockwise, that is away from the hour hand, although it is actually moving clockwise. This apparent anticlockwise rotation of the hour hand is the motion relative to the minute hand. It is the difference between the two motions that creates the relative motion.