Logo
Home Study Material Contact Search
AI Chat FREE
  1. sciences
  2. physics
  3. find the moment of inertia of a circular disk of r

Find the moment of inertia of a circular disk of radius R and mass M that...

90.2K

Verified Solution

Question

Physics

Find the moment of inertia of a circular disk of radius R andmass M that rotates on an axis passing through its center. [Answer:½ MR2]
Step 1: Pictorial representation: Sketch a neat picture torepresent the situation.

Step 2: Physical representation: 1) Cut the disk into many smallrings as it has the circular symmetry. 2) Set up your coordinatesystem and choose its origin at the pivot point (or the axlelocation) for convenience. Then choose a not-special piece as arepresentative of those small masses dm:



Step 3: Determine the moment of inertia of this representativesmall mass and evaluate the integral for the total moment ofinertia:










Step 4: Use the parallel-axis theorem to determine the moment ofinertia of the disk around an axis located at the edge of the disk.Then compare the two moments of inertia and explain how the resultsmake sense to you.

Answer & Explanation Solved by verified expert
4.4 Ratings (592 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Biology
1.2K views

What have you learned that has changed your mind about diabetes and diabetes management?

Physics
1.2K views

1) Describe what polarization means in the context of electric charges. Generally, under what circumstances would I...

Physics
1.2K views

The Quest For Perpetual Motion It has been a tenet of physics that it is not...

Mechanical Engineering
1.2K views

In one or two sentences describe the corrosion failure mode. What is one visual cue to...

General Management
1.2K views

1. Summarize Globalization 3.0 21st century. 2. Would you say that IKEA success has been sustainable?...

Basic Math
1.2K views

(a) f(x) =-1/3xg(x) =-1/3xf(g(x)) = g (f(x)) = fand g are inverses of each...

Basic Math
1.2K views

The Health Club offers a silver membership and a gold membership. The table contains information...

Calculus
1.2K views

Finding a difference quotient f(x+h)-f(x)/h, where h ? 0, for the function below. f(x)=3x-6 Simplify...

Accounting
1.2K views

02 You oversee the $250 petty cash for your company. When an employee...

Accounting
1.2K views

This is a full project that needs the following entries recorded - General Ledger, General...

Accounting
1.2K views

Aquarius Game Inc has finished a new video game, Triathlon Challenge. Management is now considering...

Accounting
1.2K views

Explain ratio analysis as an analytical procedure used by auditors. Give examples of the ratios...