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Inertia force 
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#1
Jul1806, 12:22 AM

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in the vibration theory of a spring mass system the text says that the mass is acted upon by three forces
1)spring forcei understand this 2)damping forcein understand this 3)inertia forcei don't understand this From where this inertia force We need to apply force to accelerate a mass that is called inertia. But what is this "inertia force" concept 


#2
Jul1806, 06:09 AM

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Think about what the meaning of inertia is. What does Newton's first law say? The inertial force is going to be the forces due to the mass of the object and it's resistance to changes in its motion. The initial acceleration term in the ODE is the inertial term.



#3
Jul1806, 07:24 AM

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In fact, the idea was to use the concepts of STATICS to introduce dynamics. In statics, the forces on an object have to balance. That means: you sum all forces, and you have to find zero. It's how you calculate, say, the load on a pillar holding a bridge or something. If you want to use that same rule with objects in motion, it doesn't work anymore. Well, it only works for objects in uniform, straight motion, but not for any accelerated motion. In that case, the sum of forces didn't sum to 0 anymore. People used to statics found that mind shaking. So a trick was invented: introduce an "inertia force" which is equal to MINUS the mass times the acceleration. NOW, the sum of all forces, including this inertia force, equals zero (haha). Of course, for people not having done a lot of statics calculations before being introduced to Newton's dynamics, this is a totally incomprehensible act, because for them, "forces" are a way to calculate accelerations. It's a book keepers' device, in order not to have to write out Newton's second law, but to be able to use the STATICS equation F_tot = 0 in a situation where it is not really appropriate anymore. 


#4
Jul1806, 10:30 AM

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Inertia force
http://www.geocities.com/physics_wor...tial_force.htm 


#5
Jul1806, 10:51 AM

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However, it can be seen of course as an inertial force in a frame FIXED TO THE MASS (so that the mass is always at rest). This is nothing else but d'Alembert's force of course (or Newton's 2nd law): static equilibrium *in the frame in which the object is at rest* needs the application of an inertial force in order to make the static equilibrium come out correctly. However, things are upsidedown now, because usually, an inertial force is a fictive term one has to add to the right side of "Newton's second law" when applied in a noninertial frame (where it shouldn't be applied  so this fictive term corrects for the error in the first place of trying to apply Newton's second law in a noninertial frame), WHEN KNOWING THE MOTION OF THE FRAME WRT AN INERTIAL FRAME. So it is a property of the frame (which has been defined wrt an inertial frame) that the transformation of Newton's second law takes up extra terms on the right side. But in this particular case, *we don't know how the frame (fixed to the mass) is going to move*. We adapt its movement, in such a way that the inertial force will compensate perfectly all other forces, so as to KEEP the object at rest in the frame. 


#6
Jul1806, 11:17 AM

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In basic vibration theory, the springmassdamper systems FBDs that I have ever seen were not referenced to the mass, they referenced the Earth. I don't think the noninertial frame angle is what is being asked about here.



#7
Jul1806, 11:26 AM

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Pete 


#8
Jul1806, 01:48 PM

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But a typical application is this: Consider a block B1 with mass m1 on a frictionless horizontal surface, connected with a rope to a block B2 with mass m2. The rope is guided over a pulley, and the block B2 is hanging in midair. Let it go. What is the force acting on block B1 through the rope ? Second question: instead of hanging a block B2 on the rope, pull with a force F = g m2 on the rope. Is the situation different ? Someone trained in statics would think that both situations are identical: the force of gravity acting on block B2 is g m2, and this is the force on the rope, and hence block B1 feels (through the rope) a force m2.g. But BZZZT. The block B2 is FALLING, so it is accelerating, with an acceleration a, downward. (a is not equal to g, because it is held back somewhat by the rope) And here comes our force of inertia of d'Alembert: the block B2 accelerating downwards with acceleration a, one has to introduce an extra force on it, equal to m2.(a). So there are now 3 forces acting on the block B2: gravity (m2.g), the rope, F_rope, and d'Alemberts' force, m2 (a). And these have to be in "equilibrium, so: F_rope + m2.g  m2.a = 0, or F_rope = m2 (a  g). This F_rope is the force of the rope on B2, so the force on the rope is minus this, m2 (g  a). So the force on block B1 is smaller than m2.g. Eh. What a clumsy way of dealing with the problem ! But it illustrates that the force in the rope is not equal to m2.g. 


#9
Jul1806, 05:51 PM

P: 2,954

Thanks for reminding me vanesch. And yes, this is used when deriving the Lagrange equations when using d'Alembert's Principle Pete ps  I recommend that you don't place words in all capitals when you wishe to emphasize something. Rather italisize it by placing the term inbetween the italics delimeters. Otherwise you come across as yelling. 


#10
Jul1806, 09:54 PM

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#11
Jul1806, 10:23 PM

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D'Alembert created a fictitious force (m.a, for constant mass) which is placed in a direction opposite to the direction of motion. This allows the body to be considered in equilibrium, & for a freebodydiagram to be constructed. This is called the 'inertia force'. Divide by mass & we have inertial acceleration.
For fluid elements, this acceleration is the 'substantial derivative', or 'total derivative'. Alternative forms can be considered for variable mass. A neat connection between kinetics & kinematics. 


#12
Apr2309, 04:41 PM

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#13
Apr2309, 04:52 PM

P: 4,663

This reminds me of the question on my graduate student Prelim Orals to solve the problem of two masses, M1 and M2, connected by a spring of spring constant k and spinning in free space. So there was also another force. Was it centrifugal or centripital? I forget.



#14
Apr2409, 04:24 AM

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centrifugal was for hydraulics if i remember right..so i think it might be centripital..



#15
Apr2409, 05:46 AM

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Centrifugal force, on the other hand, is an inertial pseudoforce that is introduced when viewing things from a rotating (and thus noninertial) frame so that Newton's laws may be applied, as explained by vanesch (almost three years ago!). So if you analyze the spinning masses from the rotating frame, you would have a centrifugal force acting outward on each mass. 


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