Select all the correct statements below about a particle curvilinear motion in n-t coordinate system :_____________ A. The total acceleration is the vector sum of an and at. B. The normal component of acceleration an represents the time rate of change in the magnitude of velocity. C. The normal acceleration an is not always toward the center of curvature. D. The tangential component of acceleration at represents the time rate of change in the magnitude of velocity.
Select all the correct statements below about a particle curvilinear motion in n-t coordinate system :_____________ A. The total acceleration is the vector sum of an and at. B. The normal component of acceleration an represents the time rate of change in the magnitude of velocity. C. The normal acceleration an is not always toward the center of curvature. D. The tangential component of acceleration at represents the time rate of change in the magnitude of velocity.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Select all the correct statements below about a particle curvilinear motion in n-t coordinate system :_____________
| A. |
The total acceleration is the |
|
| B. |
The normal component of acceleration an represents the time rate of change in the magnitude of velocity. |
|
| C. |
The normal acceleration an is not always toward the center of curvature. |
|
| D. |
The tangential component of acceleration at represents the time rate of change in the magnitude of velocity. |
This diagram illustrates a particle in a curvilinear motion, showing the relationship between the total acceleration (a), the normal acceleration component (\(a_n\)), and the tangential acceleration component (\(a_t\)).
- \(a_n\): Normal acceleration component, pointing towards the center of curvature.
- \(a_t\): Tangential acceleration component, along the tangent to the path at the particle's position.
- \(a\): Total acceleration, which is the resultant vector of \(a_n\) and \(a_t\).
**Select all the correct statements below about a particle curvilinear motion in n-t coordinate system:**
- [ ] A. The total acceleration is the vector sum of \( \mathbf{a_n} \) and \( \mathbf{a_t} \).
- [ ] B. The normal component of acceleration \( \mathbf{a_n} \) represents the time rate of change in the magnitude of velocity.
- [ ] C. The normal acceleration \( \mathbf{a_n} \) is not always toward the center of curvature.
- [ ] D. The tangential component of acceleration \( \mathbf{a_t} \) represents the time rate of change in the magnitude of velocity.
**Explanation of the Diagram:**
The provided diagram visualizes the particle moving along a curved path and the vectors representing the components of acceleration. The normal acceleration vector (\(a_n\)) is directed towards the center of the curvature of the path, while the tangential acceleration vector (\(a_t\)) lies along the tangent to the path at the particle's given position.
**Analysis of Statements:**
- **Statement A:** True. The total acceleration is indeed the vector sum of the normal and tangential components, i.e., \( \mathbf{a} = \mathbf{a_n} + \mathbf{a_t} \).
- **Statement B:** False. The normal component of acceleration \( \mathbf{a_n} \) does not represent the time rate of change in the magnitude of velocity but rather the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0daff6b4-7b3b-4798-aa81-781ef422795b%2Fbf75d88d-b7fb-447f-af7b-b4d00ffabc66%2Fetytge8_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Understanding Particle Curvilinear Motion in n-t Coordinate System**
When studying the motion of a particle in a curvilinear path, it is essential to decompose the motion into normal (n) and tangential (t) components. Below are statements about this topic, and you need to select the correct ones:
This diagram illustrates a particle in a curvilinear motion, showing the relationship between the total acceleration (a), the normal acceleration component (\(a_n\)), and the tangential acceleration component (\(a_t\)).
- \(a_n\): Normal acceleration component, pointing towards the center of curvature.
- \(a_t\): Tangential acceleration component, along the tangent to the path at the particle's position.
- \(a\): Total acceleration, which is the resultant vector of \(a_n\) and \(a_t\).
**Select all the correct statements below about a particle curvilinear motion in n-t coordinate system:**
- [ ] A. The total acceleration is the vector sum of \( \mathbf{a_n} \) and \( \mathbf{a_t} \).
- [ ] B. The normal component of acceleration \( \mathbf{a_n} \) represents the time rate of change in the magnitude of velocity.
- [ ] C. The normal acceleration \( \mathbf{a_n} \) is not always toward the center of curvature.
- [ ] D. The tangential component of acceleration \( \mathbf{a_t} \) represents the time rate of change in the magnitude of velocity.
**Explanation of the Diagram:**
The provided diagram visualizes the particle moving along a curved path and the vectors representing the components of acceleration. The normal acceleration vector (\(a_n\)) is directed towards the center of the curvature of the path, while the tangential acceleration vector (\(a_t\)) lies along the tangent to the path at the particle's given position.
**Analysis of Statements:**
- **Statement A:** True. The total acceleration is indeed the vector sum of the normal and tangential components, i.e., \( \mathbf{a} = \mathbf{a_n} + \mathbf{a_t} \).
- **Statement B:** False. The normal component of acceleration \( \mathbf{a_n} \) does not represent the time rate of change in the magnitude of velocity but rather the
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