Question

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????

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.

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 uniform disk of mass Mdisk = 4 kg and radius R =
0.24 mhas a small block of mass mblock = 2.2 kg on its
rim. It rotates about an axis a distance d = 0.16 m from its center
intersecting the disk along the radius on which the block is
situated.
What is the moment of inertia of the block about the rotation
axis?
What is the moment of inertia of the disk about the rotation
axis?
When...

Two disks are rotating about the same axis. Disk A has a moment
of inertia of 3.1 kg · m2 and an angular velocity of
+8.0 rad/s. Disk B is rotating with an angular velocity of -9.3
rad/s. The two disks are then linked together without the aid of
any external torques, so that they rotate as a single unit with an
angular velocity of -2.2 rad/s. The axis of rotation for this unit
is the same as that for...

Two disks are rotating about the same axis. Disk A has a moment
of inertia of 3.7 kg · m2 and an angular velocity of +7.7 rad/s.
Disk B is rotating with an angular velocity of -10.4 rad/s. The two
disks are then linked together without the aid of any external
torques, so that they rotate as a single unit with an angular
velocity of -2.5 rad/s. The axis of rotation for this unit is the
same as that for...

A horizontal turntable is made from a uniform solid disk and is
initially rotating with angular velocity of 7.1 rad/s about a fixed
vertical axis through its center. The turntable has a radius of
0.23 m and a moment of inertia of 0.04761 kg m2 about
the rotation axis.
A piece of clay, initially at rest, is dropped onto the
turntable and sticks to it at a distance d= 0.16 m from its center
as shown in the figure. The...

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...

In the figure, a small disk of radius r=1.00 cm has been glued
to the edge of a larger disk of radius R=6.00 cm so that the disks
lie in the same plane. The disks can be rotated around a
perpendicular axis through point O at the center of the larger
disk. The disks both have a uniform density (mass per unit volume)
of 1.40 × 103 kg/m3 and a uniform thickness of 7.00 mm. What is the
rotational inertia...

In the figure, a small disk of radius r=2.00 cm has
been glued to the edge of a larger disk of radius R=7.00
cm so that the disks lie in the same plane. The disks can be
rotated around a perpendicular axis through point O at the
center of the larger disk. The disks both have a uniform density
(mass per unit volume) of 1.40 × 10^3 kg/m3 and a
uniform thickness of 6.00 mm. What is the rotational inertia...

A ceiling fan consists of a small cylindrical disk with 5 thin
rods coming from the center. The disk has mass md = 3 kg
and radius R = 0.24 m. The rods each have mass mr = 1.2
kg and length L = 0.72 m.
1)
What is the moment of inertia of each rod about the axis of
rotation?
kg-m2
2)
What is the moment of inertia of the disk about the axis of
rotation?
kg-m2
3)
What...

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