Question

Find the moment of inertia of a uniform hollow sphere of mass M, inner radius r, and outer radius R > r, about an axis through the center of mass. Consider your answer for the cases r → 0 and r → R. Does the result reduce correctly? Explain.

Answer #1

A hollow metal sphere has inner radius
a and outer radius
b. The hollow sphere has
charge
+2
Q. A point charge
+ Q sits at the center of the
hollow sphere.
A)Determine the
magnitude of the electric field in the region
r?a. (The correct answer does not
depend on:
Q, ??0, r.)
B) Determine the
magnitude of the electric field in the region
a<r<b
C)Determine the magnitude of the electric field in the
region
r?b
D)How much charge is...

A hollow, conducting sphere with an outer radius of 0.260 m and
an inner radius of 0.200 m has a uniform surface charge density of
+6.47 × 10−6 C/m2. A charge of -0.400 μC is now introduced into the
cavity inside the sphere.
a)What is the new charge density on the outside of the
sphere?
b)Calculate the strength of the electric field just outside the
sphere
c)What is the electric flux through a spherical surface just
inside the inner surface...

A hollow, conducting sphere with an outer radius of 0.260 m and
an inner radius of 0.200 m has a uniform surface charge density of
+6.37 × 10−6 C/m2. A charge of -0.700 μC is now introduced into the
cavity inside the sphere. a) What is the new charge density on the
outside of the sphere? b) Calculate the strength of the electric
field just outside the sphere. c) What is the electric flux through
a spherical surface just inside...

to which physical quantity in linear motion os the quantity
"moment of inertia" analogous to in rotational motion
a. kinetic energy
b. velocity
c. mass
d. momentum
part b. consider a uniform circular disk of mass M and radius R.
what formula would you use to calculate its moment of inertia
relative to an axis perpendicular to the plane the disk and passing
through its center?
I =
Part c. consider a ring of mass M and inner radius R1...

A hollow sphere and a solid sphere, both of mass M and radius R,
are each spinning about an axis through their centers with the same
angular speed. If the same braking torque is applied to each, which
takes longer to come to a stop?
A. hollow sphere B. solid sphere C. They both come to a stop in
an equal amount of time.

Derive the equation for moment of inertia of a uniform disk with
the axis of rotation through its center. The disk has a mass M and
a radius R. Record your answer in terms of M and R.
Hint: ??=2????

Find the moment of inertia of a uniform square lamina of side
a and mass m
about a diagonal.
Find the angular momentum about the origin of the square when
it is rotating with angular speed ω about
(a) the x-axis and (b) the diagonal through the
origin.
Find the kinetic energy in the two cases above
Find the principal moment of inertia of a square plate about a
corner.
Find the principal axis associated with each principal moment
of...

A sphere of solid aluminum (r = 2.7 g/cm3 ) has a radius R, a
mass M, and a moment of inertia I0 about its center. A second
sphere of solid aluminum has a different mass M’ with a radius 2R.
What is the moment of inertia of the second sphere about its center
I in terms of the first sphere I0? Mass should not appear in your
answer (4 points).

A hollow, conducting sphere with
an outer radius of 0.260m and an inner radius of 0.207m has a
uniform surface charge density of +6.79

Consider an insulating sphere of radius 5 cm surrounded by a
conducting sphere of inner radius 22 cm and outer radius 25 cm.
Furthermore, suppose that the electric field at a point 13 cm from
the center is measured to be 1540 N/C radially inward while the
electric field at a point 44 cm from the center is 90 N/C radially
outward.
1. Find the charge on the insulating sphere. Answer in units of
C.
2.Find the net charge on...

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