is moment of inertia,a vector or a scalar quantity?

Answer 1

it is not a vector nor a scalar but a tensor quantity!

Answer 2

Moment of inertia is neither a scalar, nor a vector, as it does not completely follow the characterstic of either of the two (is'nt it?)
In fact, there are some physical quantities which are neither scalars nor vectors, but a sort of 'hybrid' of the two. Physicists have placed them in a category called 'tensors'. Moment of inertia, pressure, stress, density, dielectric current, density, etc. are tensors.

Answer 3

The moment of inertia has two forms, a scalar form I (used when the axis of rotation is known) and a more general tensor form that does not require knowing the axis of rotation. The scalar moment of inertia I is often called simply the "moment of inertia".

It is the rotational analogue to mass. It should not be confused with the second moment of area (area moment of inertia), which is used in bending calculations.

area moment of inertia is with respect to a horizontal axis through the centroid of the given shape, unless otherwise specified.

a tensor is a certain kind of geometrical entity and array concept. It generalizes the concepts of scalar, vector (spatial) and linear operator, in a way that is independent of any chosen frame of reference.

Answer 4

Moment of inertia is the diagonal component of inertia tensor. When we use a symmetric axis the off diagonal elements cancel and we get a scalar. It is equivalent to the contraction of a second order tensor to get a scalar. Moment of inertia defined normally is about an axis and hence it is a scalar.

Answer 5

The moment of inertia has two forms, a scalar form I (used when the axis of rotation is known) and a more general tensor form that does not require knowing the axis of rotation.

Answer 6

When you know the axis of rotation, it is a scalar quantity defined by:

(Double integral of) g(x,y)*d(x,y)^2 [with respect to x and y]

in the plane (just replace x,y for different coordinate systems and/or working in space instead of the plane)

where g(x,y) gives you the density of the point considered and d(x,y) gives you it's distance from the axis or point of rotation. Please note that the integration range for your variables and the values of your function are supplied by your model. A simple example is a disk of uniform density and mass 1 rotating around its center using polar coordinates:

M.I. = Integral of (1 * r^2 * r * dr * dtheta), r from 0 to a, theta from 0 to 2*pi.

Evaluating the double integral gives

M.I. = 2*pi*a^4/4 = pi*a^4/2

where a is the radius of the disk.

Good luck with your studies!

Answer 7

M.I. =mas x square of the distance from the rotational axis
simply it's a scalar quantity.

Answer 8

it should be vector because it is a product of vector and scalar

Answer 9

It's a second order tensor (i.e. a matrix)