A small metal cylinder rests on a circular turntable that is rotating horizontally at a constant rate, as illustrated in (Figure 1). Figure < 1 of 2 > Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram? (Figure 2) ▸ View Available Hint(s) ▾ O a Ob Oc Od O. Submit Part B Let R be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location R/2 from the center of the turntable. Which of the fo statements accurately describe the motion of the cylinder at the new location? Check all that apply. ▸ View Available Hint(s) The speed of the cylinder has decreased. The speed of the cylinder has increased. The magnitude of the acceleration of the cylinder has decreased. The magnitude of the acceleration of the cylinder has increased. The speed and the acceleration of the cylinder have not changed.

College Physics
11th Edition
ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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**Educational Content: Rotational Motion and Forces**

**Introduction**

A small metal cylinder rests on a circular turntable that rotates horizontally at a constant rate, as illustrated in Figure 1.

**Part A: Analysis of Vectors**

**Question:** Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram? (Refer to Figure 2)

- a
- b
- c
- d
- e

(**Note:** Click to view available hints)

**Part B: Impact of Changing Position**

**Question:** Let \( R \) be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location \( R/2 \) from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location? Check all that apply.

- The speed of the cylinder has decreased.
- The speed of the cylinder has increased.
- The magnitude of the acceleration of the cylinder has decreased.
- The magnitude of the acceleration of the cylinder has increased.
- The speed and the acceleration of the cylinder have not changed.

(**Note:** Click to view available hints)

**Figure Description**

- **Figure 1:** This figure shows the top view of a turntable with a small metal cylinder placed on it. The turntable is depicted as rotating, indicated by a circular arrow around its edge.

Understanding the vectors and the effects of changing positions relative to the rotational axis is crucial for analyzing rotational dynamics. Use the above figure references and questions to explore how vectors describe motion in rotational systems and how distance from the center affects speed and acceleration.
Transcribed Image Text:**Educational Content: Rotational Motion and Forces** **Introduction** A small metal cylinder rests on a circular turntable that rotates horizontally at a constant rate, as illustrated in Figure 1. **Part A: Analysis of Vectors** **Question:** Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram? (Refer to Figure 2) - a - b - c - d - e (**Note:** Click to view available hints) **Part B: Impact of Changing Position** **Question:** Let \( R \) be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location \( R/2 \) from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location? Check all that apply. - The speed of the cylinder has decreased. - The speed of the cylinder has increased. - The magnitude of the acceleration of the cylinder has decreased. - The magnitude of the acceleration of the cylinder has increased. - The speed and the acceleration of the cylinder have not changed. (**Note:** Click to view available hints) **Figure Description** - **Figure 1:** This figure shows the top view of a turntable with a small metal cylinder placed on it. The turntable is depicted as rotating, indicated by a circular arrow around its edge. Understanding the vectors and the effects of changing positions relative to the rotational axis is crucial for analyzing rotational dynamics. Use the above figure references and questions to explore how vectors describe motion in rotational systems and how distance from the center affects speed and acceleration.
The image illustrates five diagrams (a to e) that depict the relationships between force (\(\vec{F}\)), velocity (\(\vec{v}\)), and acceleration (\(\vec{a}\)).

Diagram a:
- \(\vec{F}\) (red arrow) points to the right.
- \(\vec{v}\) (green arrow) points to the right.
- \(\vec{a}\) (orange arrow) points to the right.

Diagram b:
- \(\vec{F}\) (red arrow) points upward.
- \(\vec{v}\) (green arrow) points to the right.
- \(\vec{a} = 0\) indicating zero acceleration.

Diagram c:
- \(\vec{F}\) (red arrow) points upward.
- \(\vec{a}\) (orange arrow) points downward.
- \(\vec{v}\) (green arrow) points to the right.

Diagram d:
- \(\vec{F}\) (red arrow) points to the right.
- \(\vec{v}\) (green arrow) points to the right.
- \(\vec{a} = 0\) indicating zero acceleration.

Diagram e:
- \(\vec{F}\) (red arrow) points downward.
- \(\vec{a}\) (orange arrow) points downward.
- \(\vec{v}\) (green arrow) points to the right.

These diagrams help illustrate various scenarios of force, velocity, and acceleration vectors and their alignment with one another.
Transcribed Image Text:The image illustrates five diagrams (a to e) that depict the relationships between force (\(\vec{F}\)), velocity (\(\vec{v}\)), and acceleration (\(\vec{a}\)). Diagram a: - \(\vec{F}\) (red arrow) points to the right. - \(\vec{v}\) (green arrow) points to the right. - \(\vec{a}\) (orange arrow) points to the right. Diagram b: - \(\vec{F}\) (red arrow) points upward. - \(\vec{v}\) (green arrow) points to the right. - \(\vec{a} = 0\) indicating zero acceleration. Diagram c: - \(\vec{F}\) (red arrow) points upward. - \(\vec{a}\) (orange arrow) points downward. - \(\vec{v}\) (green arrow) points to the right. Diagram d: - \(\vec{F}\) (red arrow) points to the right. - \(\vec{v}\) (green arrow) points to the right. - \(\vec{a} = 0\) indicating zero acceleration. Diagram e: - \(\vec{F}\) (red arrow) points downward. - \(\vec{a}\) (orange arrow) points downward. - \(\vec{v}\) (green arrow) points to the right. These diagrams help illustrate various scenarios of force, velocity, and acceleration vectors and their alignment with one another.
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