Question

The rotational inertia *I* of any given body of mass
*M* about any given axis is equal to the rotational inertia
of an *equivalent hoop* about that axis, if the hoop has the
same mass *M* and a radius *k* given by

The radius *k* of the equivalent hoop is called the
*radius of gyration* of the given body. Using this formula,
find the radius of gyration of **(a)** a cylinder of
radius 3.72 m, **(b)** a thin spherical shell of
radius 3.72 m, and **(c)** a solid sphere of radius
3.72 m, all rotating about their central axes.

Answer #1

Four objects—a hoop, a solid cylinder, a solid sphere, and a
thin, spherical shell—each have a mass of 4.06 kg and a radius of
0.253 m.
(a) Find the moment of inertia for each object as it rotates
about the axes shown in this table.
hoop
___ kg · m2
solid cylinder
___ kg · m2
solid sphere
___ kg · m2
thin, spherical shell
___ kg · m2
(b) Suppose each object is rolled down a ramp. Rank the...

Compute the rotational inertia for a spherical shell rotating
about its diameter. The mass of the shell is 10 kg and the shell
has an inner radius of 5 cm and an outer radius of 15 cm

Calculate the rotational inertia of a meter stick with mass
m=0.56 kg about an axis perpendicular to set stick and located at
the 20 cm mark. (Treat the stick as a thin rod).

Find the moment of inertia of a uniformly dense hollow cylinder
rotating about the y- axis. [Clearly define all model elements and
show all work for full credit]
Check your answer with the following limiting conditions:
- When a0 (solid disk/cylinder)
- When a ≈ b (thin hoop/cylinder)

Each of the following objects has a radius of 0.209 m and a mass
of 2.31 kg, and each rotates about an axis through its center (as
in this table) with an angular speed of 36.0 rad/s. Find the
magnitude of the angular momentum of each object. (a) a hoop kg ·
m2/s (b) a solid cylinder kg · m2/s (c) a solid sphere kg · m2/s
(d) a hollow spherical shell kg · m2/s

Calculate the rotational inertia of a meter stick, with mass
0.633 kg, about an axis perpendicular to the stick and located at
the 27.4 cm mark. (Treat the stick as a thin rod.)

Two spheres are each rotating at an angular speed of 23.7 rad/s
about axes that pass through their centers. Each has a radius of
0.360 m and a mass of 1.68 kg. However, as the figure shows, one is
solid and the other is a thin-walled spherical shell. Suddenly, a
net external torque due to friction (magnitude = 0.400 N · m)
begins to act on each sphere and slows the motion down. How long
does it take (a) the...

Consider the objects below, all of mass M and radius R (where
appropriate). They are placed on an incline plane at the same
height. Which object will roll down the incline and reach the
bottom with the greatest total energy?
a) A solid sphere
b) A thin spherical shell
c) A solid cylinder of length L
d) A cylindrical shell of length L
e) All will reach bottom with same energy
Group of answer choices
A solid sphere
A thin...

A cylinder of radius R = 50 cm has rotational inertia I. It is
rotating with angular velocity w = 2 rad / s. A bullet of mass m =
160 grams and speed v = 1500 m / s hits the cylinder at a distance
40 cm from its axis and remains there. Both the cylinder and the
bullet stop after collision. Find I in units of kg - m2.

A hoop (rotational inertia I=MR2 ) of mass M = 1.6 kg and radius
R = 50 cm is rolling on a flat surface at a center-of-mass speed of
v = 1.2 m/s. Part A The total kinetic energy of the rolling hoop
can be expressed as The total kinetic energy of the rolling hoop
can be expressed as 34Mv2 12Mv2 Mv2 56Mv2 32Mv2 Request Answer Part
B If an external force does 16 J of a positive work on...

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