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Rotational motion C. Suppose the wheel makes one complete revolution in 2 seconde 1. For each of the following points, find the change in angle (A6) of the position vector during one second (i.e., find the angle between the initial and final position vectors). point A point B gaino • point C 2. Find the rate of change in the angle for any point on the wheel.

Rotational motion C. Suppose the wheel makes one complete revolution in 2 seconde 1. For each of the following points, find the change in angle (A6) of the position vector during one second (i.e., find the angle between the initial and final position vectors). point A point B gaino • point C 2. Find the rate of change in the angle for any point on the wheel.

College Physics
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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Could you help with question C and D? 

The 1st image is just for additional info

### Rotational Motion #### C. Suppose the wheel makes one complete revolution in 2 seconds. 1. For each of the following points, find the change in angle (Δθ) of the position vector during one second (i.e., find the angle between the initial and final position vectors): - **point A** - **point B** - **point C** 2. Find the rate of change in the angle for any point on the wheel. The rate you calculated above is called the **angular speed** of the wheel, or equivalently, the magnitude of the **angular velocity** of the wheel. The angular velocity is defined to be a vector that points along the axis of rotation and is conventionally denoted by the symbol **ω** (the Greek letter omega). To determine the direction of the angular velocity vector, we imagine an observer on the axis of rotation who is looking toward the object. If the observer sees the object rotating counterclockwise, the angular velocity vector is directed toward the observer; if the observer sees it rotating clockwise, the angular velocity vector is directed away from the observer. #### D. Would two observers on either side of a rotating object agree on the direction of the angular velocity vector? Explain. Would two observers who use different points on an object to determine the angular velocity agree on the magnitude of the angular velocity vector? Explain. #### E. The diagrams at right show top and side views of the spinning wheel in part A. On each diagram, draw a vector to represent the angular velocity of the wheel. (Use the convention that ⊙ indicates a vector pointing out of the page and ⊗ indicates a vector pointing into the page.) **Diagram Explanation:** - **Top View (Left Diagram):** - Shows a circular wheel labeled with points A, B, and C. - The wheel spins counterclockwise. - The vector representing the angular velocity should be drawn as ⊙ (out of the page) due to the counterclockwise rotation from the top view. - **Side View (Right Diagram):** - Illustrates a side perspective of the wheel, showing the axis of rotation. - Points A and C are located on either side of the axis. - The angular velocity vector for the side view should also be denoted. These diagrams help in visualizing the angular velocity direction based on the rotation observed from different perspectives.
Transcribed Image Text:### Rotational Motion #### C. Suppose the wheel makes one complete revolution in 2 seconds. 1. For each of the following points, find the change in angle (Δθ) of the position vector during one second (i.e., find the angle between the initial and final position vectors): - **point A** - **point B** - **point C** 2. Find the rate of change in the angle for any point on the wheel. The rate you calculated above is called the **angular speed** of the wheel, or equivalently, the magnitude of the **angular velocity** of the wheel. The angular velocity is defined to be a vector that points along the axis of rotation and is conventionally denoted by the symbol **ω** (the Greek letter omega). To determine the direction of the angular velocity vector, we imagine an observer on the axis of rotation who is looking toward the object. If the observer sees the object rotating counterclockwise, the angular velocity vector is directed toward the observer; if the observer sees it rotating clockwise, the angular velocity vector is directed away from the observer. #### D. Would two observers on either side of a rotating object agree on the direction of the angular velocity vector? Explain. Would two observers who use different points on an object to determine the angular velocity agree on the magnitude of the angular velocity vector? Explain. #### E. The diagrams at right show top and side views of the spinning wheel in part A. On each diagram, draw a vector to represent the angular velocity of the wheel. (Use the convention that ⊙ indicates a vector pointing out of the page and ⊗ indicates a vector pointing into the page.) **Diagram Explanation:** - **Top View (Left Diagram):** - Shows a circular wheel labeled with points A, B, and C. - The wheel spins counterclockwise. - The vector representing the angular velocity should be drawn as ⊙ (out of the page) due to the counterclockwise rotation from the top view. - **Side View (Right Diagram):** - Illustrates a side perspective of the wheel, showing the axis of rotation. - Points A and C are located on either side of the axis. - The angular velocity vector for the side view should also be denoted. These diagrams help in visualizing the angular velocity direction based on the rotation observed from different perspectives.
## ROTATIONAL MOTION ### I. Motion with Constant Angular Velocity A wheel is spinning counterclockwise at a constant rate about a fixed axis. The diagram at right represents a snapshot of the wheel at one instant in time. ![Wheel spinning counterclockwise](attachment:image) #### A. Representing Velocity at Points A, B, and C - **Task**: Draw arrows on the diagram to represent the direction of the velocity for each of the points A, B, and C at the instant shown. - **Question**: Explain your reasoning. - **Follow-up Question**: Is the time taken by points B and C to move through one complete circle greater than, less than, or equal to the time taken by point A? - **Follow-up Question**: On the basis of your answer above, determine how the speeds of points A, B, and C compare. Explain. #### B. Velocity Vectors at Different Rotational Positions - **Task**: Mark the position of each of the labeled points at a later time when the wheel has completed one half of a turn. Sketch a velocity vector at each point. - **Question**: For each labeled point, how does the velocity compare to the velocity at the earlier time in part A? Discuss both magnitude and direction. #### Conceptual Question - **Question**: Is there one single linear velocity vector that applies to every point on the wheel at all times? Explain. ### Explanation of Diagrams 1. **First Diagram (Upper Right Corner)**: - Displays a top view of a wheel spinning counterclockwise around a central axis. - Labeled points A, B, and C are marked on the wheel's rim and along one of the spokes. 2. **Second Diagram (Lower Right Corner)**: - Shows the same wheel at a later time, exactly one half of a turn later.
Transcribed Image Text:## ROTATIONAL MOTION ### I. Motion with Constant Angular Velocity A wheel is spinning counterclockwise at a constant rate about a fixed axis. The diagram at right represents a snapshot of the wheel at one instant in time. ![Wheel spinning counterclockwise](attachment:image) #### A. Representing Velocity at Points A, B, and C - **Task**: Draw arrows on the diagram to represent the direction of the velocity for each of the points A, B, and C at the instant shown. - **Question**: Explain your reasoning. - **Follow-up Question**: Is the time taken by points B and C to move through one complete circle greater than, less than, or equal to the time taken by point A? - **Follow-up Question**: On the basis of your answer above, determine how the speeds of points A, B, and C compare. Explain. #### B. Velocity Vectors at Different Rotational Positions - **Task**: Mark the position of each of the labeled points at a later time when the wheel has completed one half of a turn. Sketch a velocity vector at each point. - **Question**: For each labeled point, how does the velocity compare to the velocity at the earlier time in part A? Discuss both magnitude and direction. #### Conceptual Question - **Question**: Is there one single linear velocity vector that applies to every point on the wheel at all times? Explain. ### Explanation of Diagrams 1. **First Diagram (Upper Right Corner)**: - Displays a top view of a wheel spinning counterclockwise around a central axis. - Labeled points A, B, and C are marked on the wheel's rim and along one of the spokes. 2. **Second Diagram (Lower Right Corner)**: - Shows the same wheel at a later time, exactly one half of a turn later.
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