Question

Prove the relation v=w x r

Answer 1

v=dX/dT ,w=d@/dt
where@ =angular displacement
x=displacement.
we know that x=@r........(1.) where r=radii of circle
so,
v=d(@r)/dt ..........from 1
v=d@/dTxr
v=w x r
hope it help u

Answer 2

v=wr where v is the tangential velocity, w is the rotational velocity, and r i the radius vector? From the attached image, it can be concluded that (each quantity is a vector): w=r x v, also v=w x r, and r= v x w. All three vectors are perpendicular to each other, therefore the intensity of each vector can be calculated by vector multiplication. Then (each quantity is a vector modulus): w=rv, v=wr, r=vw, this system of equations is true if w=v=r which mustn't be true. I need an explanation. What did I wrong to arrive at this incorrect equality?