LECTURE # 24|| MOMENTS OF INERTIA BY TRIPLE INTEGRALS|| EX:10.4 || PROBLEM 5|| S.M YOUSAF CALCULUS

Описание: This course is specially designed for the students of 3rd semester who are doing B.S Mathematics from Punjab University Lahore, Pakistan.
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B.S MATHEMATICS|| CHAPTER# 10 MULTIPLE INTEGRALS
COURSE CODE: MATH-202 || PUNJAB UNIVERISTY.
COURSE: MATHEMATICS B-III|| CALCULUS-II
MULTIVARIABLE CALCULUS FOR B.S MATHEMATICS
TOPIC: MOMENTS OF INERTIA VIA TRIPLE INTEGRALS.
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LECTURE # 24
In this lecture I shall discuss question number 5 of Exercise 10.4 from your text book Calculus and Analytic Geometry written by S.M YOUSAF.
Here you can learn how to find SECOND MOMENTS OF INERTIA by using triple integrals.
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Question # 5 For the right circular cone of radius ‘r’ and height ‘h’. Find the moments of Inertia with respect to
a) Its axis.
b) Any straight line through its vertex and perpendicular to the axis.
c) Any line through its center of gravity and perpendicular to its axis.
d) Any diameter of its base.
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Moments of Inertia:
Moments of inertia ‘I’ of a particle of mass ‘M’ about a line ‘L’(called Axis) is defined by
I=M d^2 where ‘d’ is the perpendicular distance between the particle and the line ‘L’.
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PARALLEL AXES THEOREM:
Sometimes we need to find M.I about an axis that does not pass through the center of mass of body, in this case to find moment of inertia about that axis we use PARALLEL AXIS theorem.
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TIME CODE FOR VIDEO CHAPTERS.
00:00 INTRODUCTION MOMENTS OF INERTIA VIA TRIPLE INTEGRALS.
02:25 CONCEPT OF SPHERICAL COORDINATES.
07:00 HOW TO GENERATE A CONE.
10:53 Question 5(a) Exercise 10.4 Calculus.
19:39 VOLUME OF CONE.
23:10 MOMENTS OF INERTIA I_z
26:14 Question 5(b) Exercise 10.4 Calculus.
34:08 DEFINITION OF MOMENTS OF INERTIA
35:38 DEFINITION OF PARALLEL AXEX THEOREM.
42:52 Question 5(c) Exercise 10.4 Calculus.
53:04 Question 5(d) Exercise 10.4 Calculus.
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TO WATCH COMPLETE PLAY LIST OF
MULTIPLE INTEGRALS CLICK ON LINK BELOW.
   • CHAPTER#10 MULTIPLE INTEGRALS. B.S MATHS  
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In this play list you can find the following contents
(1) DOUBLE INTEGRALS
(2) USE DOUBLE INTEGRALS FOR AREA UNDER THE CURVES.
(3) USE DOUBLE INTEGRALS FOR VOLUME OF SOLID.
(4) DOUBLE INTEGRALS IN POLAR COORDINATES.
(5) APPLICATIONS OF DOUBLE INTEGRALS.
(6) TRIPLE INTEGRALS.
(7) TRIPLE INTEGRALS IN CYLENDRICAL COORDINATES.
(8) TRIPLE INTEGRALS IN SPHERICAL COORDINATES.
(9) APPLICATIONS OF TRIPLE INTEGRALS.
(10) MASS, DENSITY, FIRST AND SECOND MOMENTS OF INERTIA
(11) CHANGE OF ORDER OF INTEGRATION IN DOUBLE INTEGRALS
(12) IMPORTANT FORMULAS OF MULTIPLE INTEGRALS
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My lectures have equal importance for students of all universities of Pakistan, India, Bangladesh and all other countries where universities are offering this course.
Specially my lecture may be very helpful for students of following universities of Pakistan
(1) LAHORE UNIVERISTY (2) PUNJAB UNIVERISTY (3) SARGODHA UNIVERISTY (4) FAST UNIVERISTY (5) VIRTUAL UNIVERISTY (6) BZU(BHAU DIN ZIKRIYA) UNIVERISTY (7) G.C UNIVERISTY (8) F.C COLLEGE UNIVERSITY (9) U.E.T (10) GUJRAT UNIVERSITY (11) PISHAWAR UNIVERSITY (12) SINDH UNIVERSITY (13) COMSAT (14) LUMS UNIVERSITY
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