Answer to Question #206762 in Mechanics | Relativity for sakhumzi Kwaza

Question

1.    A particle of mass m moves in the x y-plane. Its position vector as a function of time is given by  where ω = angular velocity of the Find Velocity

Answer 1

Gives

Mass (m)=m

r(t)=xi+yj

$v=r\times w$

$w=w\hat z$

We know that

$v=\begin{vmatrix} \hat i & \hat j&\hat k \\ x&y&0 \\ 0&0&w_z\\ \end{vmatrix}$

Solve it

$$v=\hat i(w_zy-0)-\hat j(xw_z-0)+\hat k(0-0)$$

$v=\hat iw_zy-\hat jxw_z$