The figure below shows four spheres at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the spheres are m₁ = 2.50 kg, m₂ = 1.50 kg, m3 = 3.70 kg, and m= 1.70 kg. y m m₁ 0 m₂ -4.00 m- A 6.00 m x m, (a) What is the moment of inertia (in kg - m²) of the system about the x-axis? kg m² 4 (b) What is the moment of inertia (in kg m²) of the system about the y-axis? kg m2 (c) What is the moment of inertia (in kg m2) of the system about an axis through O and perpendicular to the page (that is, the z-axis)? kg-m²

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 49P
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The figure below shows four spheres at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system.
The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the spheres are
m₁
= 2.50 kg, m₂ = 1.50 kg, m3 = 3.70 kg, and MA = 1.70 kg.
y
m
m₁
0
m2
4.00 m-
6.00 m
x
m3
(a) What is the moment of inertia (in kg m²) of the system about the x-axis?
9
kg .m²
A
(b) What is the moment of inertia (in kg m²) of the system about the y-axis?
kg. m²
(c) What is the moment of inertia (in kg m²) of the system about an axis through O and perpendicular to the page (that is, the z-axis)?
kg - m²
N
Transcribed Image Text:The figure below shows four spheres at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the spheres are m₁ = 2.50 kg, m₂ = 1.50 kg, m3 = 3.70 kg, and MA = 1.70 kg. y m m₁ 0 m2 4.00 m- 6.00 m x m3 (a) What is the moment of inertia (in kg m²) of the system about the x-axis? 9 kg .m² A (b) What is the moment of inertia (in kg m²) of the system about the y-axis? kg. m² (c) What is the moment of inertia (in kg m²) of the system about an axis through O and perpendicular to the page (that is, the z-axis)? kg - m² N
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