$6.50 Answer
- This tutorial hasn't been purchased yet.
- Posted on Nov 04, 2009 at 02:54:34PM
A:
Preview: ... rotation.
The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, determining the relationship between a ...
The full tutorial is about 124 words long .
$9.00 Best answer
- This tutorial hasn't been purchased yet.
- Posted on Nov 04, 2009 at 02:58:09PM
A:
Preview: ... o this l ...
The full tutorial is about 8 words long plus attachments.
Attachments:
moment%20of%20inertia.pdf (182K) (Preview)
$9.00 Moment of inertia in very simple words
- This tutorial hasn't been purchased yet.
- Posted on Nov 04, 2009 at 03:08:47PM
A:
Preview: ... results. For spheres of mass m and radius r :
The Area Moment Of Inertia of a beams cross-sectional area measures the beams ability to resist bending. The larger the Moment of Inertia the less the beam will bend.
The moment of inertia is a geometrical property of a beam and depends on a reference axis. The smallest Moment of Inertia about any axis passes throught the centroid.
For a point mass the Moment of Inertia is the mass times the square of perpendicular distance to the rotation reference axis and can be expressed as
I = m r 2 (1)
where
I = moment of inertia (lb m ft 2, kg m 2)
m = mass (lb m, kg)
r = distance between axis and rotation mass (ft, m)
Moment of Inertia - General Formula
The Inertia formula may be gen ...
The full tutorial is about 624 words long .
$9.00 tutorial for moment of inertia
- This tutorial hasn't been purchased yet.
- Posted on Nov 04, 2009 at 03:14:52PM
A:
Preview: ... t be confused with the polar moment of inertia, which is a measure of an object's ability to resist torsion (twisting). Definition A simple definition of the moment of inertia (with respect to a given axis of rotation) of any object, be it a point mass or a 3D-structure, is given by: I = \int r^2 \,dm\,\! where m is mass and r is the perpendicular distance to the axis of rotation. The (scalar) moment of inertia of a point mass rotating about a known axis is defined by I \triangleq m r^2\,\! The moment of inertia is additive. Thus, for a rigid body consisting of N point masses mi with distances ri to the rotation axis, the total moment of inertia equals the sum of the point-mass moments of inertia: I \triangleq \sum_{i=1}^{N} {m_{i} r_{i}^2}\,\! For a solid body described by a mass density function, ?(r), the moment of inertia about a known axis can be calculated by integrating the square of the distance (weighted by the mass density) from a point in the body to the rotation axis: I \triangleq \iiint_V \|\mathbf{r}\|^2 \,\rho(\mathbf{r})\,dV \! where V is the volume occupied by the object. ? is the spatial density function of the object, and r = (r,?,f), (x,y,z), or (r,?,z) is the vector (orthogonal to the axis of rotation) between the axis of rotation and the point in the body. Based on dimensional analysis alone, the moment of inertia of a non-point object must take the form: I = c\cdot M\cdot {L}^2 \,\! where M is the mass L is a length dimension taken from the centre of mass (in some cases, the length of the object is used instead.) c is a dimensionless constant called the inertial constant that varies with the object in consideration. Inertial constants are used to account for the differences in the placement of the mass from the center of rotation. Examples include: * c = 1, thin ring or thin-walled cylinder around its center, * c = 2/5, solid sphere around its center * c = 1/2, solid cylinder or disk around its center. When c is 1, the length (L) is called the radius of gyration. Parallel axis theorem:: Once the moment of inertia has been calculated for rotations about the center of mass of a rigid body, one can conveniently recalculate the moment of inertia for all parallel rotation axes as well, without having to resort to the formal definition. If the axis of rotation is displaced by a distance r from the center of mass axis of rotation (e.g., spinning a disc about a point on its periphery, rather than through its center,) the displaced and center-moment of inertia are related as follows: I_{\mathrm{displaced}} = I_{\mathrm{center}} + m r^{2}. \,\! This theorem is also known as the parallel axes rule and is a special case of Steiner's parallel-axis theorem. Composite bodies If a body can be decomposed (either physically or conceptually) into several constituent parts, then ...
The full tutorial is about 2304 words long plus attachments.
Attachments:
vi.txt (14K) (Preview)
$5.00 correct tutorial
- This tutorial hasn't been purchased yet.
- Posted on Nov 04, 2009 at 06:01:45PM
A:
Preview: ... track of radius r can be specified by the
angle, ?, made wit ...
The full tutorial is about 228 words long plus attachments.
Attachments:
moment of inertia.pdf (94K) (Preview)
$5.00 Moment of Inertia in detail
- This tutorial hasn't been purchased yet.
- Posted on Nov 10, 2009 at 08:32:31PM
A:
Preview: ... a tutorial which gives a clear idea a ...
The full tutorial is about 33 words long plus attachments.
Attachments:
moment of inertia.pdf (182K) (Preview)
Moment of Inertia Basics.doc (141K) (Preview)
$2.00 Moment of Inertia Explanation
- This tutorial hasn't been purchased yet.
- Posted on Nov 17, 2009 at 01:59:51PM
A:
Preview: ... e inertia of a rigid rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, determining the relationship between angular momentum and angular velocity , torque and angular acceleration , and several other quantities. The symbol I and sometimes J are usually used to refer to the moment of inertia.
While a simple scalar treatment of the moment of inertia suffices for many situations, a more advanced tensor treatment allows the analysis of such complicated systems as spinning tops and gyroscopic motion.
The moment of inertia of an object about a given axis describes how difficult it is ...
The full tutorial is about 581 words long .
