Question

A ceiling fan is rotating around a fixed axle as shown. The direction of angular velocity is along _______.

• A. $+\hat{j}$
• B. $-\hat{j}$
• C. $+\hat{k}$
• D. $-\hat{k}$

Answer 1

The Correct Option is D

In the given problem, the ceiling fan is rotating around a fixed axle, and the direction of angular velocity is along the axis of rotation, which is the z-axis.
Using the right-hand rule for angular velocity:
If the fan is rotating counterclockwise (when viewed from above), the direction of the angular velocity vector is along the positive z-axis.
If the fan is rotating clockwise (when viewed from above), the direction of the angular velocity vector is along the negative z-axis. Since the problem does not specify the direction of rotation, but typically, ceiling fans rotate counterclockwise when viewed from below, the direction of angular velocity is along the positive z-axis.

Thus, the correct answer is (D) \( -k \), assuming clockwise rotation.

Answer 2

In rotational motion, the direction of the angular velocity vector is determined by the right-hand rule. For a ceiling fan, if the blades are rotating counterclockwise when viewed from below (as shown in the diagram), the angular velocity vector points downward along the axis of rotation. The axis of rotation for the fan is along the \( z \)-axis, and the direction of angular velocity is along the negative \( z \)-axis, which corresponds to \( -\hat{k} \).

Thus, the direction of angular velocity is along \( -\hat{k} \), and the correct answer is \( {-\hat{k}} \).