Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 3

Why doesn't it make sense to talk about a body's rotational inertia unless you specify a rotation axis?

Short Answer

Expert verified
Rotational inertia or moment of inertia depends upon how mass is distributed with respect to the axis of rotation. Hence, without specifying a rotation axis, the rotational inertia becomes ambiguous as its value varies with different axes.

Step by step solution

01

Understanding rotational inertia

Rotational inertia, often referred to as the moment of inertia (usually denoted as \( I \)), reflects the distribution of mass in a body and its resistance to rotational motion. It is given by \( I = \sum m_{i}r_{i}^{2} \), where \( m \) is the mass of the individual particles making up the object and \( r \) is the distance of each particle from the axis of rotation.
02

Dependencies of rotational inertia

From the above formula, it is evident that if we change the axis of rotation, the distance (\( r \)) of particles from the axis will also vary. This directly affects the moment of inertia. Thus, moment of inertia is not solely a property of the mass of the objects but also depends on how that mass is distributed relative to the axis of rotation.
03

Significance of specifying a rotation axis

If we don't specify the axis of rotation, the moment of inertia becomes ambiguous. The same body could have different moments of inertia for different axes of rotation. Therefore, to discuss a body's rotational inertia, it's essential to mention the axis of rotation.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A solid cylinder and a hollow cylinder of the same mass and radius are rolling along level ground at the same speed. Which has more kinetic energy?

A compact disc (CD) player varies the rotation rate of the disc in order to keep the part of the disc from which information is being read moving at a constant linear speed of \(1.30 \mathrm{m} / \mathrm{s} .\) Compare the rotation rates of a 12.0 -cm-diameter CD when information is being read (a) from its outer edge and (b) from a point \(3.75 \mathrm{cm}\) from the center. Give your answers in \(\mathrm{rad} / \mathrm{s}\) and \(\mathrm{rpm}\).

A point on the rim of a rotating wheel has nonzero acceleration, since it's moving in a circular path. Does it necessarily follow that the wheel is undergoing angular acceleration?

A solid 2.4 -kg sphere is rolling at \(5.0 \mathrm{m} / \mathrm{s}\). Find (a) its translational kinetic energy and (b) its rotational kinetic energy.

Express each of the following in radians per second: (a) 720 rpm: (b) \(50^{\circ} \mathrm{M} ;\) (c) 1000 rev/s; (d) 1 rev/year (Earth's angular speed in its orbit).
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Physics of Motion

Read Explanation

Quantum Physics

Read Explanation

Wave Optics

Read Explanation

Rotational Dynamics

Read Explanation

Modern Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free