Question

A sphere with radius 0.250 m has density ρ that decreases with distance r from the center of the sphere according to ρ=2.75×103kg/m3−(9.00×103kg/m4)r . Part A: Calculate the total mass of the sphere. Express your answer with the appropriate units. M = ?; Try Again Part B :Calculate the moment of inertia of the sphere for an axis along a diameter. Express your answer with the appropriate units.

Answer #1

A sphere with radius 0.150 m has density ρ that decreases with
distance r from the center of the sphere according to
ρ=3.25×103kg/m3−(8.50×103kg/m^4)r .
a)Calculate the total mass of the sphere. Express your answer
with the appropriate units.
B)Calculate the moment of inertia of the sphere for an axis
along a diameter. Express your answer with the appropriate
units.

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).

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 sphere of radius R has total mass M and density function given
by ρ = kr, where r is the distance a point lies from the centre of
the sphere. Give an expression for the constant k in terms of M and
R.

You place a sphere of radius R=1.54 m and of density ρ =
0.75g/cm3 in a pool of clean water. The sphere begins to float and
a portion of the sphere begins to show. (a) What is the height of
the portion that shows above the water? What minimum force should
you press on the sphere to make it sink completely in the pool?
Show your complete work step by step.

You place a sphere of radius R=1.54 m and of density ρ =
0.75g/cm^3 in a pool of clean water. The sphere begins to float and
a portion of the sphere begins to show. What is the height of the
portion that shows above the water? What minimum force should you
press on the sphere to make it sink completely in the pool? Show
your complete work step by step.

3. Consider a solid hemisphere of radius R, constant mass
density ρ, and a total mass M. Calculate all elements of the
inertia tensor (in terms of M and R) of the hemisphere for a
reference frame with its origin at the center of the circular base
of the hemisphere. Make sure to clearly sketch the hemisphere and
axes positions.

The density of a cylinder of radius R and length l
varies linearly from the central axis where ρ1=500
kg/m3 to the value ρ2=3ρ1. If
R=.05 m and l= .1 m, find:
a. The average density of the cylinder over the radius.
b. The average density over its volume.
c. the moment of inertia of the cylinder about its central
axis.

A 0.250-kg wooden rod is 1.35 m long and pivots at one end. It
is held horizontally and then released.
Part A
What is the angular acceleration of the rod after it is
released?
Express your answer to three significant figures and include
appropriate units.
Part B
What is the linear acceleration of a spot on the rod that is
1.13 m from the axis of rotation?
Express your answer to three significant figures and include
appropriate units.
Part C...

A solid insulating sphere has total charge Q and radius R. The
sphere's charge is distributed uniformly throughout its volume. Let
r be the radial distance measured from the center of the
sphere.
If E = 440 N/C at r=R/2, what is E at r=2R?
Express your answer with the appropriate units.

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