Sign Up

Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.

Have an account? Sign In

Have an account? Sign In Now

Sign In

Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.

Sign Up Here

Forgot Password?

Don't have account, Sign Up Here

Forgot Password

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

Have an account? Sign In Now

You must login to ask question.(5)

Forgot Password?

Need An Account, Sign Up Here

Please briefly explain why you feel this question should be reported.

Please briefly explain why you feel this answer should be reported.

Please briefly explain why you feel this user should be reported.

Sign InSign Up

ITtutoria

ITtutoria Logo ITtutoria Logo

ITtutoria Navigation

  • Python
  • Java
  • Reactjs
  • JavaScript
  • R
  • PySpark
  • MYSQL
  • Pandas
  • QA
  • C++
Ask A Question

Mobile menu

Close
Ask a Question
  • Home
  • Python
  • Science
  • Java
  • JavaScript
  • Reactjs
  • Nodejs
  • Tools
  • QA
Home/ Questions/Two identical uniform solid spheres areattached by a solid uniform thin rod, as shown in the figure...
Next
Answered
ptntuto
  • 7
ptntuto
Asked: April 13, 20222022-04-13T06:37:43+00:00 2022-04-13T06:37:43+00:00In: Physics

Two identical uniform solid spheres areattached by a solid uniform thin rod, as shown in the figure…

  • 7

. Advertisement .

..3..

Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in the figure. The rod lies on a line connecting the centers of mass of the two spheres. The axes A, B, C, and D are in the plane of the page (which also contains the centers of mass of the spheres and the rod), while axes E and F (represented by black dots) are perpendicular to the page.

......... ADVERTISEMENT .........

..8..

Two%20identical%20uniform%20solid%20spheres%20areattached%20by%20a%20solid%20uniform%20thin%20rod,%20as%20shown%20in%20the%20figure.%20Therod%20lies%20o...
Rank the moments of inertia of this object about the axes indicated.
Rank from largest to smallest. To rank items as equivalent, overlap them.A,B,C,D,E,F
Revelant knowledge
The moment of inertia of a rigid body, also known as mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia, is a quantity that determines the torque required for a desired angular acceleration about a rotational axis, in the same way that mass determines the force required for a desired acceleration. It relies on the mass distribution of the body and the axis chosen, with higher moments necessitating more torque to affect the rate of rotation.
moments of inertia
  • 2 2 Answers
  • 15 Views
  • 0 Followers
  • 0
Answer
Share
  • Facebook
  • Report

2 Answers

  • Voted
  • Oldest
  • Recent
  • Random
  1. Best Answer
    ptntuto
    2022-04-27T10:08:10+00:00Added an answer on April 27, 2022 at 10:08 am

    Answer: C = F > B > E = A > D

    Explanation:

    The moment of inertia I is given by
    I = mr2

    Where: m is the mass and r is the distance of the center of mass from the axis rotation.
    Since the mass is the same for all cases, the differences in the moment of inertia in the different axes will depend on the distance r from the axis of rotation.
    The moment of inertia at C and F are the largest because those are the axes that are farthest from the center of mass. Next to C and F is B. Then followed by E and A. The axis where the moment of inertia is the least is at D because the distance from the axis of rotation exceeds the radius of the balls.

    • 19
    • Reply
    • Share
      Share
      • Share on Facebook
      • Share on Twitter
      • Share on LinkedIn
      • Share on WhatsApp
      • Report
  2. Joseph Brown
    2022-04-13T06:37:46+00:00Added an answer on April 13, 2022 at 6:37 am
    Concepts and Reason

    This question’s main concept is Moment of Inertia for a uniform solid sphere.

    Calculate the moment of inertia for all spheres around axis F. Then, apply the theorem to the rest of axis. Finally, rank them according to their moment of inertia.

    Fundamentals

    Consider two identical solid spheres with mass m, radius r, and attached to a rod of l.

    The moment of inertia (equa_tag_0)

    [katex]{I_1} = \frac{2}{5}m{r^2}[/katex]

    Here, m is a mass, r the radius and [katex]{I_1}[/katex] are the values.

    The moment of inertia [katex]{I_2}[/katex]

    [katex]{I_2} = \frac{1}{{12}}M{l^2}[/katex]

    Here M is the rod’s mass, l the length and [katex]{I_2}[/katex] are the parameters.

    The theorem about parallel axis says that the moment inertia for a rigid object about an axis is equal the sum of its moment of inertia about an axis passing through its center of mass and the product mass of the object with squared of the distance between the axes.

    Locate the moment of inertia around the axis , and .

    Let F be the axis that passes through the center of the sphere [katex]{S_1}[/katex]

    The moment of inertia (equa_tag_7)

    [katex]{I_{1F}} = \frac{2}{5}m{r^2}[/katex]

    Theorem of parallel-axis for moment of inertia [katex]{I_{2F}}[/katex]

    [katex]\begin{array}{c}\\{I_{2F}} = \frac{2}{5}m{r^2} + m{\left( {r + l + r} \right)^2}\\\\ = \frac{2}{5}m{r^2} + m{\left( {2r + l} \right)^2}\\\end{array}[/katex]

    Apply the theorem for parallel axis to the moment of inertia [katex]{I_{3F}}[/katex]

    [katex]{I_{3F}} = \frac{1}{{12}}M{l^2} + M{\left( {r + \frac{l}{2}} \right)^2}[/katex]

    Total moment of inertia (equa_tag_13)

    [katex]\begin{array}{c}\\{I_F} = {I_{1F}} + {I_{2F}} + {I_{3F}}\\\\ = \frac{2}{5}m{r^2} + \left\{ {\frac{1}{{12}}M{l^2} + M{{\left( {r + \frac{l}{2}} \right)}^2}} \right\} + \left\{ {\frac{2}{5}m{r^2} + m{{\left( {2r + l} \right)}^2}} \right\}\\\\ = \frac{4}{5}m{r^2} + m{\left( {2r + l} \right)^2} + \frac{1}{{12}}M{l^2} + M{\left( {r + \frac{l}{2}} \right)^2}\\\end{array}[/katex]

    Symmetry means that the moment of inertia for the first sphere around a central axis of the plane of paper parallel to A is the same as the moment for axis F.

    Total moment of inertia (equa_tag_15)

    [katex]\begin{array}{c}\\{I_A} = {I_{1A}} + {I_{2A}} + {I_{3A}}\\\\ = \left\{ {\frac{2}{5}m{r^2} + m{{\left( {r + \frac{l}{2}} \right)}^2}} \right\} + \frac{1}{{12}}M{l^2} + \left\{ {\frac{2}{5}m{r^2} + m{{\left( {r + \frac{l}{2}} \right)}^2}} \right\}\\\\ = \frac{4}{5}m{r^2} + 2m{\left( {r + \frac{l}{2}} \right)^2} + \frac{1}{{12}}M{l^2}\\\\ = \frac{4}{5}m{r^2} + m{\left( {2r + l} \right)^2} + \frac{1}{{12}}M{l^2}\\\end{array}[/katex]

    Here [katex]{I_{1A}}[/katex]

    The moment of inertia [katex]{I_B}[/katex]

    [katex]\begin{array}{c}\\{I_B} = {I_{1B}} + {I_{2B}} + {I_{3B}}\\\\ = \left\{ {\frac{2}{5}m{r^2} + m{{\left( {r + l} \right)}^2}} \right\} + \frac{1}{{12}}M{l^2} + M{\left( {\frac{l}{2}} \right)^2} + \left\{ {\frac{2}{5}m{r^2} + m{r^2}} \right\}\\\\ = \frac{4}{5}m{r^2} + m{\left( {r + l} \right)^2} + \frac{1}{{12}}M{l^2} + M\frac{{{l^2}}}{4} + m{r^2}\\\end{array}[/katex]

    The rod’s central axes are A, and . Because of symmetry, there is no moment of inertia for the system around axes A or E.

    The moment of inertia for the system around axes C and F are the same.

    Because the distance perpendicular to the axis from the axis rotation is never greater than the radius of one of the balls, the axis D has the lowest moment of inertia.

    The order of highest to lowest is:

    [katex]{\rm{C}} = {\rm{F}} > {\rm{B}} > {\rm{A}} = {\rm{E}} > {\rm{D}}[/katex]Ans:

    The order in which axis are arranged from largest to most is [katex]{\rm{C}} = {\rm{F}} > {\rm{B}} > {\rm{A}} = {\rm{E}} > {\rm{D}}[/katex].

    • 23
    • Reply
    • Share
      Share
      • Share on Facebook
      • Share on Twitter
      • Share on LinkedIn
      • Share on WhatsApp
      • Report

Leave an answer
Cancel reply

You must login to add an answer.

Forgot Password?

Need An Account, Sign Up Here

Sidebar

Ask A Question
  • How to Split String by space in C++
  • How To Convert A Pandas DataFrame Column To A List
  • How to Replace Multiple Characters in A String in Python?
  • How To Remove Special Characters From String Python

Explore

  • Home
  • Tutorial

Footer

ITtutoria

ITtutoria

This website is user friendly and will facilitate transferring knowledge. It would be useful for a self-initiated learning process.

@ ITTutoria Co Ltd.

Tutorial

  • Home
  • Python
  • Science
  • Java
  • JavaScript
  • Reactjs
  • Nodejs
  • Tools
  • QA

Legal Stuff

  • About Us
  • Terms of Use
  • Privacy Policy
  • Contact Us

DMCA.com Protection Status

Help

  • Knowledge Base
  • Support

Follow

© 2022 Ittutoria. All Rights Reserved.

Insert/edit link

Enter the destination URL

Or link to existing content

    No search term specified. Showing recent items. Search or use up and down arrow keys to select an item.