Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks

Exams
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology

EXAM TYPES

GCSE

IGCSE

AS

A Level

International A Level

University Admissions Tests

GCSE SUBJECTS

GCSE 1

GCSE 2

GCSE 3

GCSE 4

GCSE 5

SOME-TEXT

IGCSE SUBJECTS

IGCSE 1

AS SUBJECTS

AS 1

A Level SUBJECTS

A Level 1

International A Level SUBJECTS

International A Level 1

University Admissions Tests SUBJECTS

University Admissions Tests 1
Features
Features

Discover all of these amazing features with a free account.

Flashcards

Vaia AI

Notes

Study Plans

Study Sets
What’s new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
Resources
Discover

All the hacks around your studies and career - in one place.

Find a job

Find a degree

Student Deals

Magazine

Mobile App
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

Job Board
The largest student job board with the most exciting opportunities.

Vaia Deals
Verified student deals from top brands.

Our App
Discover our mobile app to take your studies anywhere.

Go to App

Learning Materials

Features

Discover

Chapter 9: Q.72 (page 230)

A uniform solid bar with mass m and length L rotates with angular velocity v about an axle at one end of the bar. What is the bar’s kinetic energy?

Short Answer

Expert verified

The total kinetic energy of the bar is $\frac{1}{6} (m ω^{2} L^{2}) .$

Step by step solution

01

Content Introduction

The formula to find kinetic energy for the small element of bar is

$d K = \frac{1}{2} v^{2} d m$

here, $d K$ is the kinetic energy of the small element of bar, $v$ is linear velocity, $d m$ is mass element of the same.

02

Content Explanation

Integrate the kinetic energy of each small element of the bar to find the total kinetic energy,

$K = \int_{0}^{L} d K K = \int_{0}^{L} \frac{1}{2} v^{2} d m K = \int_{0}^{L} \frac{1}{2} {(ω x)}^{2} d m$

The formula to find the small mass is

$d m = λ d x$

Substitute

$K = \int_{0}^{L} \frac{1}{2} {(ω x)}^{2} d m K = \frac{1}{2} ω^{2} λ \int_{0}^{L} {(x)}^{2} d x K = \frac{1}{6} ω^{2} λ L^{3} K = \frac{1}{6} m ω^{2} L^{2}$

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

The left end of a spring is attached to a wall. When Bob pulls on the right end with a 200 N force, he stretches the spring by 20 cm. The same spring is then used for a tug-of-war between Bob and Carlos. Each pulls on his end of the spring with a 200 N force.
How far does the spring stretch? Explain.

A $25$ kg air compressor is dragged up a rough incline from $\vec{r_{1}} = (1.3 \hat{i} + 1.3 \hat{j})$ m to $\vec{r_{2}} = (8.3 \hat{i} + 2.9 \hat{j})$ m, where the $y -$ axis is vertical. How much work does gravity do on the compressor during this displacement?

Susan’s $10$ kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled $30 °$ above the floor. The tension is a constant $30$ N and the coefficient of friction is $0.20$ . Use work and energy to find Paul’s speed after being pulled $3.0$ m.

At what speed does a 1000 kg compact car have the same kinetic energy as a 20,000 kg truck going 25 km/h?

The driver of a car traveling at 60 mph slams on the brakes, and the car skids to a halt. What happened to the kinetic energy the car had just before stopping?

See all solutions

Recommended explanations on Physics Textbooks

Electrostatics

Read Explanation

Classical Mechanics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Force

Read Explanation

Particle Model of Matter

Read Explanation

Further Mechanics and Thermal 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