Concept explainers
Figure 10-13 shows four masses that are held at the corners of a square by a very light frame. What is the moment of inertia of the system about an axis perpendicular to the page (a) through A and (b) through B?
Fig. 10-13
(a)
The moment of inertia of the system shown in Fig. 10.13, about an axis perpendicular to the page through A.
Answer to Problem 57SP
Solution:
Explanation of Solution
Given data:
The system of four masses are shown as follows:
Formula used:
Write the expression of moment of inertia of a mass system about an axis is given as follows.
Here,
Write the expression of Pythagoras theorem in right angled triangle to find the distance of point mass from the axis.
Here,
Explanation:
Redraw the diagram of the system show provided in the question:
From fig. 1, infer that all the point masses are at equal distance from the axis perpendicular to page through A. Let the distance of point masses from the axis be
The expression of distance of point masses from axis perpendicular to page through A is,
Here,
Substitute
Solve for
The expression of moment of inertia about a given axisfor a mass system is as follows,
Since, the perpendicular distances of all the point masses from the given axis are equal, therefore, the expression of the distance of all point masses from the given axis is,
Substitute
Substitute
Conclusion:
The moment of inertia of the system about an axis perpendicular to the page through A is
(b)
The moment of inertia of the system shown in Fig. 10-13, about an axis perpendicular to the page through B.
Answer to Problem 57SP
Solution:
Explanation of Solution
Given data:
The system of four masses that are held at the corners of a square by a very light frame as shown in fig. 1.
Formula used:
Write the expression of moment of inertia about a given axis.
Here,
Write the expression of Pythagoras theorem in right angled triangle to find the distance of point mass from the axis.
Here,
Explanation:
From fig. 1, infer that the distance of point mass
The expression of distance of point mass,
Here,
Substitute
The expression of Pythagoras theorem in right angled triangle to find the distance of point mass from the axis B.
Here,
Substitute
Solve for
Further, solve the expression.
The expression of moment of inertia about a given axis is,
Substitute
Substitute
Conclusion:
The moment of inertia of the system about an axis perpendicular to the page through B is
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Chapter 10 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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