What is the meaning of relative motion equation in a rigid body?

[g460cbk]

Hi I have learned Dynamics in school;;;

I have problem in relative motion chapter[rigid body & fixed position]

upload some picture.

first picture is my textbook page. In picture. textbook says to me that V(b1)=V(A)

because this particle is rigid body and point doesn't change their position each other on surface. So their moving is just rotating.

and second picture say that meaning of relative motion equation in rigid body.

My question :::::

why did't textbook say V(A)=V(b1)+some element heading to V(b2) ?

In my think it is possible V(A) has some element about b(2) axis (first picture)

but in my textbook V(A) has only b(1) direction. It make me crazy.

help me~~~~~~~~``

 

[tiny-tim]

welcome to pf!

hi g460cbk! welcome to pf!

(try using the X₂ icon just above the Reply box )

V_B/A (the velocity of B relative to A) must be perpendicular to AB

this is because AB² is constant, ie AB.AB = constant, so AB.d(AB)/dt = 0, ie AB.V_B/A = 0

AB lies entirely along b₁ (this is how unit vector b₁ is defined), so V_B/A lies entirely along b₂

 

[g460cbk]

thank you for your help

I never know (d/dt)AB^2=0 .

you're genious!