**Transcription of Educational Website Content:**---**Rotational Motion and Angular Speed Analysis****Problem Statement:**Using a sign convention that counterclockwise (CCW) is positive and clockwise (CW) is negative, consider a wheel spinning around the z-axis (or its axis of rotation). What does it mean when angular acceleration (\(\alpha\) < 0) and angular velocity (\(\omega\) > 0)?**Options:**(a) The angular speed is increasing in the CCW direction and the wheel rotational motion is decelerating.(b) The angular speed is increasing in the CW direction and the wheel rotational motion is decelerating.(c) The angular speed is decreasing in the CCW direction and the wheel rotational motion is accelerating.(d) The angular speed is decreasing in the CW direction and the wheel rotational motion is accelerating.(e) The angular speed is increasing in the CCW direction and the wheel rotational motion is accelerating.(f) The angular speed is increasing in the CW direction and the wheel rotational motion is accelerating.(g) The angular speed is decreasing in the CCW direction and the wheel rotational motion is decelerating.**Diagram Explanation:**The accompanying diagram shows a flat, circular wheel viewed from an angle. It is positioned on the coordinate system defined by x, y, and z axes. The z-axis is vertically aligned, and there is an arrow indicating rotation around the z-axis in a counterclockwise direction, illustrating the positive direction of angular velocity. The wheel is depicted as a flat disc, emphasizing the radial distance \(r\) of any point on the wheel from the axis of rotation.---**Understanding the Concepts:**- **Angular Acceleration (\(\alpha\)):** The rate of change of angular velocity. A negative value (\(\alpha < 0\)) indicates that the wheel is slowing down in the counterclockwise direction or speeding up in the clockwise direction.- **Angular Velocity (\(\omega\)):** A positive value (\(\omega > 0\)) in this context indicates that the wheel is currently rotating in the counterclockwise direction.**Conclusion:**Choosing the correct statement requires understanding how negative angular acceleration affects current positive angular velocity. Evaluate which option fits these conditions.--- **Text Transcription for Educational Website:****Question 4: Sign Convention for Rotational Motion**Using a sign convention that counterclockwise (CCW) is positive and clockwise (CW) is negative, and a wheel is spinning around the z-axis (or its axis of rotation), what does it mean when angular acceleration (α) is greater than 0 and angular velocity (ω) is greater than 0?Options:(a) The angular speed is increasing in the CCW direction and the wheel's rotational motion is decelerating.(b) The angular speed is increasing in the CW direction and the wheel's rotational motion is decelerating.(c) The angular speed is decreasing in the CCW direction and the wheel's rotational motion is accelerating.(d) The angular speed is decreasing in the CW direction and the wheel's rotational motion is accelerating.(e) The angular speed is increasing in the CCW direction and the wheel's rotational motion is accelerating.(f) The angular speed is increasing in the CW direction and the wheel’s rotational motion is accelerating.(g) The angular speed is decreasing in the CCW direction and the wheel’s rotational motion is decelerating.**Diagram Explanation:**The diagram to the right illustrates a wheel rotating around the z-axis. The z-axis is depicted as a vertical line, with the wheel lying in the xy-plane. The circular arrow around the z-axis indicates the direction of rotation, which is counterclockwise (CCW). The radius of the wheel is labeled as 'r'. The axes are marked as 'x', 'y', and 'z' to define the three-dimensional space in which the wheel rotates.

Answered: Image /qna-images/answer/cf3616e8-fa94-4164-b931-2e53668e9dab.jpgSo, options d,e are correct.

4. Using a sign convention that CCW is positive and CW is negative and a wheel is spinning around the z-axis (or its axis of rotation), what does it mean when a > 0 and w > 0? (a) The angular speed is increasing in the CCW direction and the wheel rotational motion is decelerating. (b) The angular speed is increasing in the CW direction and the wheel rotational motion is decelerating (c) The angular speed is decreasing in the CCW direction and the wheel rotational motion is accelerating (d) The angular speed is decreasing in the CW direction and the wheel rotational motion is accelerating (e) The angular speed is increasing in the ccW direction and the wheel rotational motion is accelerating. (f) The angular speed is increasing in the CW direction and the wheel rotational motion is accelerating. (g) The angular speed is decreasing in the CCW direction and the wheel rotational motion is decelerating.

4. Using a sign convention that CCW is positive and CW is negative and a wheel is spinning around the z-axis (or its axis of rotation), what does it mean when a > 0 and w > 0? (a) The angular speed is increasing in the CCW direction and the wheel rotational motion is decelerating. (b) The angular speed is increasing in the CW direction and the wheel rotational motion is decelerating (c) The angular speed is decreasing in the CCW direction and the wheel rotational motion is accelerating (d) The angular speed is decreasing in the CW direction and the wheel rotational motion is accelerating (e) The angular speed is increasing in the ccW direction and the wheel rotational motion is accelerating. (f) The angular speed is increasing in the CW direction and the wheel rotational motion is accelerating. (g) The angular speed is decreasing in the CCW direction and the wheel rotational motion is decelerating.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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