Question

Consider a lamina in the shape of a half annulus with inner radius 5 and outer radius 9. The mass density at any point is directly proportional to the distance to the origin. Compute the moment of inertia with respect to the diameter.

Don’t leave the proportionality constant in the answer. You may, however, leave m in your answer, so you may need to compute that as well. What does diameter mean for a half annulus? It means the same thing that it would be if it were a half disk.

Answer #1

Consider the hemispherical shell of inner radius 3 and outer
radius 7. The mass density at any point P(x,y,z) is directly
proportional to the square of the distance from P to the
origin.
Set up an integral in an appropriate coordinate system for the
moment of inertia about the z-axis. Simplify your integrand as much
as possible, but do not evaluate the integral.

A hollow sphere of inner radius 5.1 cm and outer radius
7.0 cm floats half submerged in a liquid of density 640
kg/m3. What is the mass of the
sphere?
(in kg)
A: 4.60×10-1
B: 6.11×10-1
C: 8.13×10-1
D: 1.08
E: 1.44
calculate the density of the material of which
the sphere is made.
(in kg/m^3)
A: 5.22×102
B: 7.57×102
C: 1.10×103
D: 1.59×103
E: 2.31×103

A compound disk of outside diameter 160 cm is made up of a
uniform solid disk of radius 32.0 cm and area density 4.70 g/cm2
surrounded by a concentric ring of inner radius 32.0 cm , outer
radius 80.0 cm , and area density 1.80 g/cm2 .
Find the moment of inertia of this object about an axis
perpendicular to the plane of the object and passing through its
center.
Please make sure for the answer to be correct and...

A large wooden turntable in the shape of a flat uniform disk has
a radius of 1.65 m and a total mass of 135 kg. The turntable is
initially rotating at 3.10 rad/s about a vertical axis through its
center. Suddenly, a 65.5-kg parachutist makes a soft landing on the
turntable at a point near the outer edge.
(a) Find the angular speed of the turntable after the
parachutist lands. (Assume that you can treat the parachutist as a
particle.)...

Moment of Inertia
To find the moment of inertia of different objects and to
observe the changes in angular acceleration relative to changing
moments of inertia.
To also learn how to use calipers in making precise
measurements
The momentum of inertia of an object is calculated as
I=∑mr^2
If the object in question rotates around a central point, then
it can be considered a "point mass", and its moment of inertia is
simply, I=mr^2 where r is from the central point...

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