For the outlined sphere model of a water molecule consisting of two small spheres with the mass m= 3 g and one large sphere with the mass M=16-m, the moments of inertia are to be calculated in relation to the mutually perpendicular axes of rotationx, y and z. The z axis is perpendicular to the plane of the drawing and, like the x axis and the y axis, should run through the center of mass of the sphere model. The connections drawn in blue should have no mass, and the spheres should be assumed to have point masses

For the outlined sphere model of a water molecule consisting of two small spheres with the mass m= 3 g and one large sphere with the mass M=16-m, the moments of inertia are to be calculated in relation to the mutually perpendicular axes of rotationx, y and z. The z axis is perpendicular to the plane of the drawing and, like the x axis and the y axis, should run through the center of mass of the sphere model. The connections drawn in blue should have no mass, and the spheres should be assumed to have point masses

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

For the outlined sphere model of a water molecule
consisting of two small spheres with the mass m= 3
g and one large sphere with the mass M=16m, the
moments of inertia are to be calculated in relation
to the mutually perpendicular axes of rotation x, y
and z. The z axis is perpendicular to the plane of
the drawing and, like the x axis and the y axis,
should run through the center of mass of the
sphere model. The connections drawn in blue
should have no mass, and the spheres should be
assumed to have point masses

m
М 316-m
m
a) State where the center of mass of the sphere
model is located (e.g. relative to the position of the
large, red sphere).
b) Calculate the moments of inertia related to the
x-, the y- and the z-axis, all through the mean-of-
mass-
should run point.
2 cm
3,2 cm

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