Question

A rigid body rotates with 50 rad/sec about the axis 𝑥 = 𝑦 = 𝑧. Find the velocity and the acceleration of a point P of the solid. Application for P(1,1,0).

Answer 1

$r=\frac{\sqrt{\begin{vmatrix} 1& 1 \\ 1 & 1 \end{vmatrix}^2+\begin{vmatrix} 1& 0 \\ 1 & 1 \end{vmatrix}^2+\begin{vmatrix} 1& 0 \\ 1 & 1 \end{vmatrix}^2}}{\sqrt{1^2+1^2+1^2}}=\sqrt{\frac 23},$

$v=\omega r=50\cdot \sqrt{\frac 23}\approx 41~\frac ms,$

$a=\omega^2 r=50^2\cdot \sqrt{\frac 23}\approx 2000~\frac{m}{s^2}.$