Shohag 10.01.03.117
-
Upload
mahbub-romit -
Category
Technology
-
view
263 -
download
0
description
Transcript of Shohag 10.01.03.117
![Page 1: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/1.jpg)
Ahsanullah University of Science And Technology
1
Prepared By Course no: CE 416
![Page 2: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/2.jpg)
:Objectives Introduction of Moment of Inertia Polar moment of inertia Radious of Gyration Moment of inertia of composite bodies Parallel axis theorm Perpendicular axis theorm
![Page 3: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/3.jpg)
MOMENT OF INERTIA
The product of the elemental area and square of the The product of the elemental area and square of the perpendicular distance between the perpendicular distance between the centroids centroids of area of area and the axis of reference is the “Moment of Inertia” and the axis of reference is the “Moment of Inertia” about the reference axis. about the reference axis.
IIxxxx = ∫dA. y = ∫dA. y22
IIyyyy = ∫dA. x = ∫dA. x22
x
dAY
x
y
![Page 4: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/4.jpg)
Fig: Relation between Moment of inertia (I) and angular velocity (w)
![Page 5: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/5.jpg)
Moment of Inertia of a Disk and a Ring : A wooden disk and a metal ring with the same diameter and equal mass roll with
different accelerations down an inclined plane. Now, if both are rolled along the lecture bench by being given an equal impulse, the metal ring will continue to roll longer than the disk because of its greater moment of inertia. However, when the ring and disk are released simultaneously from the same height on an inclined plane, the wooden disk reaches the bottom first due to its lesser moment of inertia.
![Page 6: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/6.jpg)
Polar Moment of Inertia
• The polar moment of inertia is an important parameter in problems involving torsion of cylindrical shafts and rotations of slabs.
dArJ 20
• The polar moment of inertia is related to the rectangular moments of inertia,
xy II
dAydAxdAyxdArJ
222220
![Page 7: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/7.jpg)
Radius of Gyration
Frequently tabulated data related to moments of inertia will be presented in terms of radius of gyration.
m
IkormkI 2
m = Mass of the body
K= Radious of Gyration
Where
![Page 8: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/8.jpg)
Moment of inertia of ’ :composite area s
![Page 9: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/9.jpg)
Parallel Axis Theorem
• The moment of inertia about any axis parallel to and at distance d away from the axis that passes through the centre of mass is:
• Whereo IG= moment of inertia for mass centre G
o m = mass of the bodyo d = perpendicular distance between the parallel axes.
2mdII GO
![Page 10: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/10.jpg)
Perpendicular Axis Theorem:
yxz III
For flat objects the rotational moment of inertia of the axes in the plane is related to the moment of inertia perpendicular to the plane.
M
Ix = (1/12) Mb2
Iy= (1/12) Ma2
a
b
Iz = (1/12) M(a2 + b2)
![Page 11: Shohag 10.01.03.117](https://reader036.fdocuments.in/reader036/viewer/2022070304/54cd912d4a7959ca738b46d2/html5/thumbnails/11.jpg)