when inertia can act as athe mass ,force and generate momentu, the why another word called mass moment of inertia. how is it different from inertia.because the momemtum has been generated because of mass and velocity hence generates force.this is how the inertia behaves. even though why we use the terms called 'moment of inertia" & 'mass momet of inertia'. what is the exact difference between them
Inertia is resistance to linear acceleration by an applied force. Moment of inertia is resistance to angular acceleration by an applied torque. In other words, the former makes it difficult to push something; the latter to rotate it.
can you elobrate please i need some more explaination regarding:- inertia moment of inertia mass moment of inertia
Actually, they are quite the same and inertia has been properly define in the second post. The only difference is that moment of inertia really is expressed as a tensor, in it's most geneal form. This tensor expresses how mass (ie inertia) is distributed throughout the volume of an object. You need to think of a matrix of which the components contain numbers, ie mass-values. Each components designates the mass of that object in a certain direction (xx,xy,xz : the directions of the top row of a 3 by 3 matrix, ya see ?). Eg, a boiled egg moves differently compared to an unboiled egg :) marlon
Making the spinning of an egg a good way to test if it is boiled or not. Is it not an important distinction that assigning a moment of inertia only makes sense for a system in a state of rotation? [EDIT To Clarify:] Since the axis in question is defined as being that of rotation.
Well, making this distiction is mathematically not really accurate because in the case of a non rotating object, the inertia tensor reduces to a tensor of rank 0, ie a scalar or a number . marlon
Thats cheating :P. Anyway, I disagree that such is not mathematically accurate since the concept of number in mathematics is one which is dependant on domain. That the complex field exists does not preclude the use of reals where appropriate simply because one is a subset of the other. Nonetheless, I meant a conceptual and not a mathematical distinction. An example of my meaning would be that I feel that it is alot of unessesary extra mental baggage to state that an object which is not rotating is rotating with an angular velocity of 0 and has an angular momentum of no angular momentum. :P I'll note also that while all scalars are numbers, all numbers are not scalars.
Defining a moment of inertia only requires picking a reference point. Call this z. Then [tex] I_{ij}(z) := \int d^{3}x \, (x-z)_{i} (x-z)_{j} \rho(x) [/tex] To be completely proper, this is the second moment of the mass density. The first moment is [tex] I_{i}(z) := \int d^{3}x \, (x-z)_{i} \rho(x) [/tex] This is closely related to the center-of-mass position. Higher moments can also be defined, but are generally not as useful. This concept of taking integrals of a function against succesively higher powers of its argument is found all over physics and math. Moments are often discussed in the context of probability distributions, for example. They also show up when finding the forces between two widely separated charged (and/or massive) particles. Edit: This definition is a bit different than the most common one, but the remarks I gave still hold whichever version you prefer.
It might be helpful to consider the moment of inertia as a quantity which is defined relative to a particular line, not to a particular point. It then becomes a scalar, measuring the torque that has to be applied to start the object rotating around that line. Every tiny piece of mass in the object contributes a certain amount to the total moment of inertia. This amount is proportional to the mass itself and to its perpendicular distance to the line. The reason is plain. Every tiny piece of mass contributes to the angular momentum (or moment of momentum). Its contribution is proportional to the vector product of its radius vector and its momentum. The latter is proportional to its mass and velocity. Its velocity, however, is the angular velocity times the perpendicular distance to the rotation axis. Dividing everything by the angular velocity yields the mement of inertia. However, this is only true if the speeds are nonrelativistic, i.e. much smaller than the speed of light, c. For relativistic speeds, the momentum is no longer proportional to the speed, v, but to v/sqrt(1 - vv/cc). The total angular momentum is therefore larger than calculated by multiplying the moment of inertia and the angular velocity. Relativistic speeds can occur if the rotating object is very large, or if the rotation is very swift, or both.
Moment of inertia is a way to make rotational kinematics analagous to translational motion because, for example: instead of using force we use torque which relies on the radius, so we must change everything else in accordance. i.e. Since force is a change in momentum over time, torque is a change in anqular momentum over time. Torque is (r)adius times the change in linear momentum/time(force); linear momentum is mv; v is rw; momentum is mrw. w being angular velocity. Then angular momentum is then mrrw. Since we want an analogy to translational momentum we say that w(angular velocity) is analogous to v(linear velocity) and mrr is analogous to mass. mrr being the moment of inertia. mr^2 if you want.