A small particle is placed inside the frictionless, semicircular tube of radius R shown in the figure below and released. Using angular momentum methods, show that the particle's equation of motion is given by 0 + (g/R) sin(0) = 0. Hint: Start with dHo/dt = EM₁ R e
A small particle is placed inside the frictionless, semicircular tube of radius R shown in the figure below and released. Using angular momentum methods, show that the particle's equation of motion is given by 0 + (g/R) sin(0) = 0. Hint: Start with dHo/dt = EM₁ R e
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
Related questions
Question
![**Problem Statement:**
A small particle is placed inside the frictionless, semicircular tube of radius \( R \) shown in the figure below and released. Using angular momentum methods, show that the particle’s equation of motion is given by:
\[
\ddot{\theta} + \left( \frac{g}{R} \right) \sin(\theta) = 0
\]
**Hint:** Start with \(\frac{dH_0}{dt} = \Sigma M_0\).
**Diagram Explanation:**
The diagram illustrates a semicircular tube with a radius \( R \). A small particle is shown inside the tube. The particle is situated on the inner surface and is denoted as a black dot. The semicircle is oriented such that the central axis \( O \) is vertical. An angle \( \theta \) is shown from the vertical line to the radius extending to the particle. This angle represents the angular displacement of the particle concerning the center of the semicircle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa487fd1f-659d-4c4f-ad85-f8cf24cc282d%2Fe5fae535-3c08-4bd8-a18b-8d9223ec8f83%2Fvu8byr6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A small particle is placed inside the frictionless, semicircular tube of radius \( R \) shown in the figure below and released. Using angular momentum methods, show that the particle’s equation of motion is given by:
\[
\ddot{\theta} + \left( \frac{g}{R} \right) \sin(\theta) = 0
\]
**Hint:** Start with \(\frac{dH_0}{dt} = \Sigma M_0\).
**Diagram Explanation:**
The diagram illustrates a semicircular tube with a radius \( R \). A small particle is shown inside the tube. The particle is situated on the inner surface and is denoted as a black dot. The semicircle is oriented such that the central axis \( O \) is vertical. An angle \( \theta \) is shown from the vertical line to the radius extending to the particle. This angle represents the angular displacement of the particle concerning the center of the semicircle.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY