**Pendulum Description and Analysis** The illustration showcases a pendulum which is composed of a uniform disk. The disk has a radius \( r = 15.0 \, \text{cm} \) and a mass of \( 880 \, \text{g} \). This disk is connected to a uniform rod with a length \( L = 570 \, \text{mm} \) and a mass of \( 270 \, \text{g} \). **Task Overview:** **(a) Calculate the rotational inertia of the pendulum about the pivot point.** To determine the rotational inertia, consider both the disk and the rod's contributions. Use the standard formulas for moment of inertia for a disk about its central axis and for a thin rod about one end. **(b) What is the distance between the pivot point and the center of mass of the pendulum?** This requires calculating the individual centers of mass for the disk and the rod and then finding the combined center of mass using the parallel axis theorem and center of mass formulas for a composite system. **(c) Calculate the period of oscillation.** The period of oscillation for a physical pendulum can be found using the formula: \[ T = 2\pi \sqrt{\frac{I}{mgd}} \] where \( I \) is the moment of inertia about the pivot, \( m \) is the total mass, \( g \) is the acceleration due to gravity, and \( d \) is the distance from the pivot to the center of mass of the pendulum. **Diagram Explanation:** The diagram features: - A vertical assembly with a rod and disk. - The pivot point is at the top of the rod where it attaches to a support. - The rod is angled with the disk at the bottom, perpendicular to the rod. - Vectors indicate measurements \( L \) (length of the rod) and \( r \) (radius of the disk). This setup is crucial for understanding the dynamics of pendulum motion and assists in solving the associated physics problems.
**Pendulum Description and Analysis** The illustration showcases a pendulum which is composed of a uniform disk. The disk has a radius \( r = 15.0 \, \text{cm} \) and a mass of \( 880 \, \text{g} \). This disk is connected to a uniform rod with a length \( L = 570 \, \text{mm} \) and a mass of \( 270 \, \text{g} \). **Task Overview:** **(a) Calculate the rotational inertia of the pendulum about the pivot point.** To determine the rotational inertia, consider both the disk and the rod's contributions. Use the standard formulas for moment of inertia for a disk about its central axis and for a thin rod about one end. **(b) What is the distance between the pivot point and the center of mass of the pendulum?** This requires calculating the individual centers of mass for the disk and the rod and then finding the combined center of mass using the parallel axis theorem and center of mass formulas for a composite system. **(c) Calculate the period of oscillation.** The period of oscillation for a physical pendulum can be found using the formula: \[ T = 2\pi \sqrt{\frac{I}{mgd}} \] where \( I \) is the moment of inertia about the pivot, \( m \) is the total mass, \( g \) is the acceleration due to gravity, and \( d \) is the distance from the pivot to the center of mass of the pendulum. **Diagram Explanation:** The diagram features: - A vertical assembly with a rod and disk. - The pivot point is at the top of the rod where it attaches to a support. - The rod is angled with the disk at the bottom, perpendicular to the rod. - Vectors indicate measurements \( L \) (length of the rod) and \( r \) (radius of the disk). This setup is crucial for understanding the dynamics of pendulum motion and assists in solving the associated physics problems.
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)...
Related questions
Concept explainers
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Topic Video
Question
![**Pendulum Description and Analysis**
The illustration showcases a pendulum which is composed of a uniform disk. The disk has a radius \( r = 15.0 \, \text{cm} \) and a mass of \( 880 \, \text{g} \). This disk is connected to a uniform rod with a length \( L = 570 \, \text{mm} \) and a mass of \( 270 \, \text{g} \).
**Task Overview:**
**(a) Calculate the rotational inertia of the pendulum about the pivot point.**
To determine the rotational inertia, consider both the disk and the rod's contributions. Use the standard formulas for moment of inertia for a disk about its central axis and for a thin rod about one end.
**(b) What is the distance between the pivot point and the center of mass of the pendulum?**
This requires calculating the individual centers of mass for the disk and the rod and then finding the combined center of mass using the parallel axis theorem and center of mass formulas for a composite system.
**(c) Calculate the period of oscillation.**
The period of oscillation for a physical pendulum can be found using the formula:
\[ T = 2\pi \sqrt{\frac{I}{mgd}} \]
where \( I \) is the moment of inertia about the pivot, \( m \) is the total mass, \( g \) is the acceleration due to gravity, and \( d \) is the distance from the pivot to the center of mass of the pendulum.
**Diagram Explanation:**
The diagram features:
- A vertical assembly with a rod and disk.
- The pivot point is at the top of the rod where it attaches to a support.
- The rod is angled with the disk at the bottom, perpendicular to the rod.
- Vectors indicate measurements \( L \) (length of the rod) and \( r \) (radius of the disk).
This setup is crucial for understanding the dynamics of pendulum motion and assists in solving the associated physics problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18d6601c-1264-4982-ae9d-82e3a3c3c6e6%2F0736e361-e0da-44ac-948a-5847bb26a927%2F8ncnrq_processed.png&w=3840&q=75)
Transcribed Image Text:**Pendulum Description and Analysis**
The illustration showcases a pendulum which is composed of a uniform disk. The disk has a radius \( r = 15.0 \, \text{cm} \) and a mass of \( 880 \, \text{g} \). This disk is connected to a uniform rod with a length \( L = 570 \, \text{mm} \) and a mass of \( 270 \, \text{g} \).
**Task Overview:**
**(a) Calculate the rotational inertia of the pendulum about the pivot point.**
To determine the rotational inertia, consider both the disk and the rod's contributions. Use the standard formulas for moment of inertia for a disk about its central axis and for a thin rod about one end.
**(b) What is the distance between the pivot point and the center of mass of the pendulum?**
This requires calculating the individual centers of mass for the disk and the rod and then finding the combined center of mass using the parallel axis theorem and center of mass formulas for a composite system.
**(c) Calculate the period of oscillation.**
The period of oscillation for a physical pendulum can be found using the formula:
\[ T = 2\pi \sqrt{\frac{I}{mgd}} \]
where \( I \) is the moment of inertia about the pivot, \( m \) is the total mass, \( g \) is the acceleration due to gravity, and \( d \) is the distance from the pivot to the center of mass of the pendulum.
**Diagram Explanation:**
The diagram features:
- A vertical assembly with a rod and disk.
- The pivot point is at the top of the rod where it attaches to a support.
- The rod is angled with the disk at the bottom, perpendicular to the rod.
- Vectors indicate measurements \( L \) (length of the rod) and \( r \) (radius of the disk).
This setup is crucial for understanding the dynamics of pendulum motion and assists in solving the associated physics problems.
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 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON