What is Inertia: Definition and 1000 Discussions

Inertia is the resistance of any physical object to any change in its velocity. This includes changes to the object's speed, or direction of motion.
An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed, when no forces act upon them.
Inertia comes from the Latin word, iners, meaning idle, sluggish. Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. Isaac Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:

The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.
In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" or for simpler terms, "resistance to a change in motion" (which is quantified by its mass), or sometimes to its momentum, depending on the context. The term "inertia" is more properly understood as shorthand for "the principle of inertia" as described by Newton in his first law of motion: an object not subject to any net external force moves at a constant velocity. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change.
On the surface of the Earth, inertia is often masked by gravity and the effects of friction and air resistance, both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled the philosopher Aristotle to believe that objects would move only as long as force was applied to them.The principle of inertia is one of the fundamental principles in classical physics that are still used today to describe the motion of objects and how they are affected by the applied forces on them.

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  1. S

    Polar moment of inertia in a rod?

    How is the polar moment of inertia in a rod calculated? Thanks.
  2. Puma

    Non-linear inertia from rest seems common?

    It seems to me that there are many instances of 'initial stickiness' when you move an object. Pushing a book over a table for example might be initially hard due to adhesive forces to the table which have formed over time - a plastic coating forming some kind of seal with a varnish is the...
  3. H

    A wheel with rotational inertia I = 1/2MR^2

    Homework Statement [/B] A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed W0. It is then lowered, and at the instant its edge touches the ground the speed of the axle (and CM) is zero. Initially the wheel slips when it...
  4. C

    Exploring the Concept of Center of Inertia: A Scientific Perspective

    What is the center of inertia? Is it the same as the center of mass?
  5. S

    Polar mass moment of inertia *and* simply moment of inertia

    Hi ,everyone… i wanted to clear my one confusion ,that what is actual difference between polar mass moment of inertia and simply moment of inertia…??
  6. O

    Does Pushing an Object in Space Result in Infinite Kinetic Energy?

    By Newton's second law of motion - inetia,we know that if we push a body in space it will keep moving forever (if nothing stops it) (am I wrong?) but when I think about conservation of energy law I am starting to have problems- let's say that I pushed a body in space,the energy converted into...
  7. T

    Calculating the moment of inertia of a filled cylinder

    Homework Statement For my IB higher level physics extended essay I will have to calculate the angular momentum of a cylinder rolling down a slope. The cylinder is made out of copper and will be filled with a known mass of car engine oil. I think i can obtain the angular velocity fairly easily...
  8. T

    Tensor moment of inertia -- why is there a "-" sign?

    why there is a negative sign in the tensor moment of inertia??
  9. gracy

    Moment of Inertia: Ignoring Small Bond Axis Molecule

    Why the moment of inertia of a molecule about the bond axis is small enough to ignore ?
  10. 462chevelle

    Moment of Inertia power plant energy

    Homework Statement It has been suggested that we should use our power plants to generate energy in the off-hours (such as late at night) and store it for use during the day. One idea put forward is to store the energy in large flywheels. Suppose we want to build such a flywheel in the shape of...
  11. C

    Valuations and places - decomposition and inertia group

    Hello, I feel very uncomfortable with some aspects of the theory of valuations, places, and valuation rings. Here is one of my problems : Assume that L/K is a finite Galois extension of fields, and that F is a place from K to its residual field k, whose associated valuation ring is discrete. F...
  12. R

    What is the correct way to find the inertia of a bullet entering a door?

    I am having trouble with this one problem. I have tried multiple times to solve it, but come up with the same wrong answer every time. The mistake that I may be making is in finding the Inertia of the bullet entering the door: I figured that some mass at the given radius from the hinge of the...
  13. W

    Pendulum Equilibrium: Can It Pass Balance Point Twice?

    Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first...
  14. R

    Moment of Inertia - center of a rod w/ unequal distribution

    Hello everyone! New member here, as an ME major I always seem to come across very valuable information here, so I figured I would see if possibly someone here could help me. The problem I am dealing with involves modeling a car through certain motions such as hitting a speed bump, and part...
  15. D

    Conservation of Energy falling rod

    Homework Statement A uniform ladder having mass 14kg and length 3m is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle Theta at which the bottom end A starts to lift off the ground. For calculation assume the ladder is a slender rod...
  16. andyrk

    Why Can't Moment of Inertia Exceed MR² for Solid Bodies?

    How do we know that moment of inertia cannot exceed MR2 for a solid body like solid cylinder, solid sphere, hollow sphere etc? R is the radius of the object in consideration. I know it has something to do with- that for solid bodies (in some cases hollow also) there are a lot of point masses in...
  17. A

    Cannon Ball in Space: What Happens & How Much Does It Hurt?

    What would happen if you were shot with a cannon ball in space? How badly do you reckon it would hurt, compared to if you were shot with the same cannon ball on Earth?
  18. M

    Calculating Mass Moment of Inertia for Slider Crank | Explained

    Hi, I'm sorry my question is almost identical to an unanswered question here, but I was unable to reply to it (because it is old?). I want to have the mass moment of inertia 'I'of the block C, which will be a function of theta. I am ignoring the contribution from the links.Due to the...
  19. E

    Finding Rotational Speed once the Moment of Inertia Increase

    Homework Statement A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 6.03 rad/s. Her moment of inertia about this axis is 16.1 kg·m2. A short time later the aerialist is in the straight position, as...
  20. T

    Moment of inertia of a door?

    Homework Statement A uniform, thin, solid door has height 2.2 m, width .87m and mass 23kg. Find the moment of inertia for rotation on its hinges. 2. Homework Equations I=∫x^2dm The Attempt at a Solution [/B]The way I set it up was that I made into strips of length H (height) and width dr...
  21. R

    Moment of Inertia about the CoM

    Homework Statement A puck of mass 82.0g and radius 4.09cm slides along an air table at a speed of v = 1.59m/s. It makes a glancing collision with a second puck of radius 6.97cm and mass 130g (initially at rest) such that their rims just touch. The pucks stick together and spin after the...
  22. B

    How does tension affect the motion of a hanging block on a rotating disk?

    Homework Statement This figure shows a uniform disk, with mass M = 2.5 kg and radius R = 20 cm, mounted on a fixed horizontal axle. A block with mass m = 1.2 kg hangs from a massless cord that is wrapped around the rim of the disk. Sample problem 10-8 (has picture diagram and detailed...
  23. P

    Calculating Inertia Tensor and Principal Moments for a Half Disk

    Homework Statement Half disk, radius R, mass m. I need the inertia tensor about the center of mass and then find the Principal moments of inertia about another coordinate system. Struggling with the product of inertia...
  24. L

    Non-Uniform Gear Moment of Inertia

    I'm working on a project involving analyzing the motion of a reciprocating saw. This saw converts rotational motion from an electric motor to linear motion by means of a slider crank mechanism. The power transmission goes from motor and attached driving gear, to crank, to connecting rod, to...
  25. Crush1986

    Moment of Inertia Compass Needle

    Homework Statement You place a magnetic compass on a horizontal surface, allow the needle to settle, and then give the compass a gentle wiggle to cause the needle to oscillate about its equilibrium position. The oscillation frequency is 0.321 Hz. Earth's magnetic field at the location of the...
  26. S

    Moment of inertia and angular velocity of a uniform disk

    Homework Statement Two particles, each of mass m, are attached one to each end of a diameter PQ of a uniform circular disk, of mass 4m, radius a with its centre at O. The system is free to rotate about a horizontal axis through A, a point on PQ such that OA = b as indicated in the diagram...
  27. Q

    Moment of Inertia of a rod and two spheres

    Homework Statement A barbell that consist of a long thin rod of mass M and length L is attached to two uniform spheres on each end. Both spheres have mass M and (1/3)L. The sphere on the left is hallow (spherical shell) and the sphere on the right is solid. What is the moment of inertia for...
  28. S

    Moments of Inertia of two particles

    Homework Statement Two particles, each of mass m, are attached one to each end of a diameter PQ of a uniform circular disk, of mass 4m, radius a with its centre at O. The system is free to rotate about a horizontal axis through A, a point on PQ such that OA = b as indicated in the diagram...
  29. C

    Moment of Inertia Graph

    Homework Statement The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation: rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants...
  30. D

    Calculate the moment of inertia for the system

    Homework Statement Calculate the moment of inertia for the system. The rods of length L are massless. Image here: http://imgur.com/O639ejf Homework Equations /answer[/B] I know that I=ΣMR^2 The correct answer to the problem is 32ml^2 I JUST WOULD LIKE TO SEE HOW THE PROBLEM IS DONE...
  31. L

    The moment of inertia of a rod that is rotating off the end of the rod.

    Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this: ------- | (------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen) I just have...
  32. S

    Proof of disk moment of inertia using area density

    Homework Statement Disk with radius R σ = M/A I = ∫ mr2 Homework Equations Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk. The Attempt at a Solution I = ∫mr2 σ = M/A dM =...
  33. M

    A spinning space station exhibits a change in moment of inertia.

    Homework Statement A space station shaped like a giant wheel has a radius 95.0 m and a moment of inertia of 5.03✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the...
  34. C

    Moment of Inertia of a solid sphere

    Homework Statement Taylor, Classical Mechanics Problem 10.11 ** a) Use the result of problem 10.4 (derivation of the general integral for a moment of inertia of a continuous mass distribution in spherical coordinates, using point particles) to find the moment of inertia of a uniform solid...
  35. L

    How High Must the Brass Ball Start to Complete the Loop-the-Loop?

    Hi everyone, I've been working on this problem for a while now, and I was hoping someone here could point me in the right direction. Here goes: 1. Homework Statement A solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight...
  36. Aristotle

    Question relevant to Moments of Inertia

    Homework Statement Homework Equations I= ∑ miri^2 ? The Attempt at a Solution I'm not sure on how to start this problem. How exactly do I know which one is IA, IB, IC since it didnt specify? Can somebody please hint me in solving this problem?
  37. K

    Complex Moment of Inertia Calculation

    Homework Statement I'm just looking for the proper equation to use to find the moment of inertia of a complex assembly of bodies. I'm not a student and this isn't homework, but it seemed the most relevant place to pose the question. One of my hobbies is making toys and I'm trying to calculate...
  38. mokeejoe5

    Mass, Energy & Inertia: Impact of Trapping Energy in a Box

    If you trap a lot of energy in a box does the system (box plus its contents) gain inertia and become more difficult to accelerate?
  39. B3NR4Y

    Inertia of a Giraffe in Terms of a Monkey (I'm serious)

    Homework Statement For my second thread of the day I will give the weirdest problem I've encountered in physics yet. In the mobile what is the inertia of the giraffe mgir in terms of the inertia mm of the monkey? Homework Equations I = md2 The Attempt at a Solution In the picture, the giraffe...
  40. Z

    Calculating Inertia at Output: Motor with 140gcm2 Rotor Inertia & 71:1 Gearhead

    I have a motor with rotor inertia of 140gcm2 with 71:1 gearhead. Considering this configuration what would my inertia be at the output ? 140*(1/71)2 ??
  41. M

    Calculating moment of inertia for nonuniform sphere

    Homework Statement A sphere with radius R = 0.200 m has density ρ that decreases with distance r from the center of the sphere according to \rho = 3.00 \times 10^3 \frac{kg}{m^3} - (9.00 \times 10^3 \frac{kg}{m^4})r a) Calculate the total mass of the sphere. b) Calculate the moment of inertia...
  42. N

    Moment of Inertia, working backwards

    I've to work out b & d in this equasion. I=bd^3/12 I know that the ratio between b & d in this case is 1.166 and I am given the value of I. It is an engineering problem as the software will only allow the use of square/rectangular or round section but we are using H section and we are allowed...
  43. B3NR4Y

    Ranking Rotational Inertia Task

    Homework Statement I'm given the following four structures with their rotational axes marked, I have to rank them from largest to smallest rotational inertias, I have trouble with that apparently. Homework Equations No equations are really necessary, just my book says the more mass there is...
  44. B

    Understanding Inertia: A Guide to its Uses and Importance in Physics

    The force of inertia is the property common to all bodies that remain in their state, either at rest or in motion, unless some external cause is introduced to make them alter this state.Is the concept of inertia still used? When is it useful as a fictitious force? Can you list a few situations...
  45. B

    Calculating Principle Moments of Inertia

    Hi Folks, Is it possible to calculate the principle moments of inertia acting along the principle axes of inertia given the moments of inertia and their directional vectors. Ie , I have the following information Moments of inertia ##J_1, J_2,J_3=18kgm2,15kgm2,6kgm2## and the directional...
  46. V

    Why do the works of two objects in rotation differ when friction is present?

    Hi, I would like to compute sum of work for 2 objects in rotation, look at image please. The grey disk has a rotationnal velocity of Y rd/s. Red disks turn at X rd/s in the same direction. Red disk don't turn around itself. X > Y At time 't' friction is on. The Work for torque = Torque *...
  47. P

    Moment of inertia about a ceiling fan?

    Homework Statement A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.3 kg and radius R = 0.26 m. The rods each have mass mr = 1.2 kg and length L = 0.72 m. What is the moment of inertia of each rod about the axis of rotation...
  48. S

    Estimate the mass of a spinning ice skater

    Homework Statement If you have data such as time of rotation when arms are extended and the lengths of their folded and extended arms measured from the centre of the skater. I know I1ω1=I2ω2 and can work out ω from the radius and time of rotation. Where can I go from here to estimate the mass...
  49. Hardik Batra

    How is the moment of inertia related to the square of the distance?

    Moment of inertia is I = MR2 object has more mass means more inertia and less mass means less inertia. That means moment of inertia is directly proportional to mass. But how the moment of inertia is directly proportional to the square of the distance.?
  50. M

    Moment of Inertia and energy

    Homework Statement A solid cube of wood with side 2a and mass M is resting on a horizontal surface. The cube is constraint to rotate about a fixed axis AB. A bullet of mass m and speed v is shot at the face opposite ABCD at a height of 4a/3. The bullet becomes embedded in the cube. Find the...
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