Question

Consider a rigid body rotating about a fixed axis with a constant angular speed $\omega .$ The angular velocity is represented by a vector $\omega$ of magnitude $\omega$ lying along the axis of rotation as shown in the figure. If we place the origin 0 on the axis of rotation and let $\mathbf{R}$ denote the position vector of a particle in the body, then the velocity $\mathbf{v}$ of the particle is given by $$\mathbf{v}=\boldsymbol{\omega} \times \mathbf{R}$$ Suppose that the axis of rotation is parallel to the vector $2 \mathbf{i}+2 \mathbf{j}+\mathbf{k}$. What is the speed of a particle at the instant it passes through the point $(3,5,2)$ ?

          Consider a rigid body rotating about a fixed axis with a constant angular speed $\omega .$ The angular velocity is represented by a vector $\omega$ of magnitude $\omega$ lying along the axis of rotation as shown in the figure. If we place the origin 0 on the axis of rotation and let $\mathbf{R}$ denote the position vector of a particle in the body, then the velocity $\mathbf{v}$ of the particle is given by
$$\mathbf{v}=\boldsymbol{\omega} \times \mathbf{R}$$
Suppose that the axis of rotation is parallel to the vector $2 \mathbf{i}+2 \mathbf{j}+\mathbf{k}$. What is the speed of a particle at the instant it passes through the point $(3,5,2)$ ?

Added by Elisa W.

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