What is the equation for inertia?

Answer 1

There are two laws about inertia. The First Law has no formula. It is just a statement that says "an object will continue at constant velocity ,or at rest, until a net force acts on it". This property that requires a force to change its state of motion (or rest) is called the object's "inertia". The Second Law is a formula that describes how an object will move when a net force acts on it. The formula is F = ma. Where, F, is the force and , a , is the objects acceleration. And , m , is the objects mass, which is a measure of the object's inertia. So you could write the formula as a = F/m and in this way you see if the object's mass (inertia) is increased then in order to get the same acceleration you must increase the force. These two laws describe how an object's inertia ,or mass, resists changes in its motion.

Answer 2

In America the formula for inertia = .5 mass X velocity2 OR

MASS (which equals, weight divided by grams)

times (which equals, X)

VELOCITY (which equals, feet per second divided by time)

Answer 3

DefinitionA 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:

where m is mass and r is the perpendicular distance to the axis of rotation.

Detailed analysis

The (scalar) moment of inertia of a point mass rotating about a known axis is defined by

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:

The mass distribution along the axis of rotation has no effect on the moment of inertia.

For a solid body described by a mass density function, ρ(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:

whereV is the volume occupied by the object.ρ is the spatial density function of the object, andr = (r,θ,φ), (x,y,z), or (r,θ,z) is the vector (orthogonal to the axis of rotation) between the axis of rotation and the point in the body. Diagram for the calculation of a disk's moment of inertia. Here c is 1/2 and is the radius used in determining the moment.

Based on dimensional analysis alone, the moment of inertia of a non-point object must take the form:

whereM is the massL 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.

For more examples, see the List of moments of inertia.

Parallel axis theoremMain article: 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:

This theorem is also known as the parallel axes rule and is a special case of Steiner's parallel-axis theorem.

Composite bodiesIf a body can be decomposed (either physically or conceptually) into several constituent parts, then the moment of inertia of the body about a given axis is obtained by summing the moments of inertia of each constituent part around the same given axis.[2] Equations involving the moment of inertiaThe rotational kinetic energy of a rigid body can be expressed in terms of its moment of inertia. For a system with N point masses mi moving with speeds vi, the rotational kinetic energy T equals

where ω is the common angular velocity (in radians per second). The final expression I ω2 / 2 also holds for a mass density function with a generalization of the above derivation from a discrete summation to an integration.

In the special case where the angular momentum vector is parallel to the angular velocity vector, one can relate them by the equation

where L is the angular momentum and ω is the angular velocity. However, this equation does not hold in many cases of interest, such as the torque-free precession of a rotating object, although its more general tensor form is always correct.

When the moment of inertia is constant, one can also relate the torque on an object and its angular acceleration in a similar equation:

where τ is the torque and α is the angular acceleration.Moment of inertia tensor

In three dimensions, if the axis of rotation is not given, we need to be able to generalize the scalar moment of inertia to a quantity that allows us to compute a moment of inertia about arbitrary axes. This quantity is as the moment of inertia tensor and can be represented as a symmetric positive semi-definite matrix, I. This representation elegantly generalizes the scalar case: The angular momentum vector, is related to the rotation velocity vector kinetic energy is given by

as compared with

in the scalar case.

Like the scalar moment of inertia, the moment of inertia tensor may be calculated with respect to any point in space, but for practical purposes, the center of mass is almost always used.

DefinitionFor a rigid object of N point masses mk, the moment of inertia tensor is given by,

where

and I12 = I21, I13 = I31, and I23 = I32. (Thus I is a symmetric tensor.)

Here Ixx denotes the moment of inertia around the x-axis when the objects are rotated around the x-axis, Ixy denotes the moment of inertia around the y-axis when the objects are rotated around the x-axis, and so on.

These quantities can be generalized to an object with distributed mass, described by a mass density function, in a similar fashion to the scalar moment of inertia. One then has

where is their outer product, E3 is the 3 × 3 identity matrix, and V is a region of space completely containing the object. Alternatively, the equation above can be represented in a component-based method. Recognizing that, in the above expression, the scalars Iij with are called the products of inertia, a generalized form of the products of inertia can be given as

The diagonal elements of I are called the principal moments of inertia.

Answer 4

You have to multiply each small unit of mass with the square of the distance from the axis of rotation. This requires an integration, but you can find tables which have this integral already solved for many standard shapes. For example, for a sphere, the moment of inertia is 2/5 M r2, and for a cylinder, rotating around its longitudinal axis, 1/2 M r2, where M is the total mass and r is the radius.

Answer 5

When studying physics it is important to remember formulas for movement. The formula for inertia is mass multiplied by velocity or F=ma.

Answer 6

It doesn't have a formula,

it has a measurement - mass.

Answer 7

The equation for inertia is ( I = m \times r^2 ), where I is the moment of inertia, m is the mass of the object, and r is the distance of the mass from the axis of rotation.