Determine the mass moment of inertia of the thin plate about the axis perpendicular to the...
Homework Answers
Mass moment of inertia:
It is calculated by multiplying the point mass with the square of the distance from the axis of rotation.
Parallel axis theorem:
It states that the moment of inertia about a point is equal to sum of the moment of inertia about the centroid of the section and the product of area of the body with the square of the distance between the centroid and the point.
Using the parallel axis theorem, the mass moment of inertia of a body about point O is determined as follows:
…… (1)
Here, mass moment of inertia of the body about point 
is 
, moment of inertia of the body passing through the mass center 
is 
, mass of the body is 
and distance between the parallel axes is 
.
The formula to calculate the moment of inertia of a circular disc passing through the mass center is as follows.
…… (2)
Here, mass of the circular disc is 
and radius of the circular disc is 
.
The formula to calculate the moment of inertia of a square plank passing through the mass center is as follows.
…… (3)
Here, mass of the square plank is 
and length of the square plank is 
.
As the plate consists of two parts, it can be subdivided into two segments. Consider the circular part as segment 
and the square part as segment
.
Show the schematic of segment 
of the thin plate as in Figure (1).
Calculate the mass of the segment 1.
Here, mass per unit area of the thin plate is 
, area of the segment 
is 
and radius of segment 
is 
.
Substitute 
for 
and 
for .
Calculate the moment of inertia of the segment 
passing through the mass center.
Substitute 
for 
and for .
Calculate the mass moment of inertia of segment 
about an axis perpendicular to the page and passing through point
.
Here, distance between the parallel axes for segment 
is 
.
Substitute
for 
, for and for 
.
Show the schematic of segment 
of the thin plate as in Figure (2).
Calculate the mass of the segment 2.
Here, area of the segment 
is 
and side of segment 
is 
.
Substitute for and for 
.
Calculate the moment of inertia of the segment 
passing through the mass center.
…… (4)
Here, diagonal length of the segment is 
.
Calculate the diagonal length of the segment .
Substitute 
for 
and 
for 
in Equation (4).
Calculate the mass moment of inertia of segment 
about an axis perpendicular to the page and passing through point.
Here, distance between the parallel axes for segment 
is 
.
Substitute
for 
, 
for 
and for 
.
Calculate the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point .
Substitute 
for 
and 
for 
.
The mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point 
is
.
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Determine the mass moment of inertia of the thin plate about the axis perpendicular to the...
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Problem 10.108 Part A consists of two slender rods AB and OC The which have a mass of 6 kg/m. The thin plate has a mass of 15 kg/m Suppose that a o0.5 m b"1.6 m,and r 0.1 m.(Figure 1) Determine the location of the center of mass G of the pendulum. Express your answer to three significant figures and include the appropriate units Figure fj- 10.82? 1 of 1 You have already submited this answer Enter a new answer...
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This pendulum is made from a 100 kg sphere and a 12-kg thin rod. Find the mass moment of inertia about an axis perpendicular to the page and passing through point A. Report your answer in kg-m2. A 1 m R.2 m
The wheel consists of a thin ring having a mass of 15 kgand four
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