Question

Show that the moment of inertial of a solid uniform octant of a sphere of radius a is (2/5)ma2 about an axis along one of the straight edges. (Note: This is the same formula as that for a solid sphere of the same radius.)

Answer #1

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.

A 4.8 kg uniform solid sphere has a radius of 32 cm and is
initially at rest. It is mounted so that it can rotate about an
axis throughout its center of mass. If a constant net torque of
17Nm is applied to the sphere (about its center of mass), then find
the power applied to the sphere 2.4s after it begins rotating.

Consider a solid sphere and a solid disk with the same radius
and the same mass. Explain why the solid disk has a greater moment
of inertia than the solid sphere, even though it has the same
overall mass and radius.

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.

A small solid sphere of mass M0, of radius R0, and of uniform
density ?0 is placed in a large bowl containing water. It floats
and the level of the water in the dish is L. Given the information
below, determine the possible effects on the water level L, (Answer
with R-Rises, F-Falls, U-Unchanged, Can also answer with R or U, F
or U, F or R or U), when that sphere is replaced by a new solid
sphere of...

Water Level A small solid sphere of mass M0, of radius R0, and
of uniform density ?0 is placed in a large bowl containing water.
It floats and the level of the water in the dish is L. Given the
information below, determine the possible effects on the water
level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is
replaced by a new solid sphere of uniform density.
1.The new sphere has mass M = M0 and radius R < R0...

A small solid sphere of mass M0, of radius R0, and of uniform
density ρ0 is placed in a large bowl containing water. It floats
and the level of the water in the dish is L. Given the information
below, determine the possible effects on the water level L,
(R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a
new solid sphere of uniform density. The new sphere has density ρ =
ρ0 and radius R > R0 The new...

A small solid sphere of mass M0, of radius R0, and of uniform
density ρ0 is placed in a large bowl containing water. It floats
and the level of the water in the dish is L. Given the information
below, determine the possible effects on the water level L,
(R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a
new solid sphere of uniform density.
The new sphere has mass M > M0 and density ρ = ρ0
The new...

A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
The new sphere has density ρ = ρ0 and radius R <
R0
The new...

A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Options are:
R= Rises
F= Falls
U= Unchnaged
F or U
R or U
F...

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