Inertia Definition and 1000 Threads

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.

View More On Wikipedia.org
  1. K

    Calculating Rotational Inertia of a Disk with Mass M and Radius R

    If there is a disk of mass M and radius R that is already rotating, then someone puts a block with mass m on it a meters away from the center of mass. What is the rotational inertia then? Is it I=(M+m)R^2?
  2. E

    Help with 2nd moment of inertia

    If a beam's y-y axis lies in the plane of the paper, do I use Ixx or Iyy from sections table?
  3. G

    Inertia and moving plane problem

    Hi, I have some troubles to understand the next step for the solution. If you need more informations, please let me know. 1. Homework Statement A moving vehicle of mass M is moving down an inclined plane of angle alpha with respect to the horizontal plane. What is the force indicated on the...
  4. H

    Moment of Inertia and Bike stability

    So is a Bike driver stable when the bike is running because the bike wheels has a certain moment of inertia about the horizontal axis ,which might alter(mi gets lesser) if the direction of the axis changes ? Thanks in advance
  5. K

    Distance traveled during a head on collision

    Homework Statement During the head on collision of a 1500kg car moving 20 m/s and a 2400 kg truck moving 12.5 m/s does the car move farther than, a shorter distance than, the same distance as the truck, or is this indeterminate with the given information. Homework Equations...
  6. W

    Calculating the Moment of Inertia of a loaded flywheel

    Hi, I need to calculate the moment of inertia of this flywheel so I can calculate the torque I need. T= I*alpha Attached is an image of the flywheel the cam follower that will be attached to the shaft (left shaft in this picture). When calculating the Moment of Inertia, what mass do I use...
  7. KastorPhys

    Moment of Inertia of a sphere with different methods

    Hi everyone, I am trying to find out the Moment of Inertia of a sphere which is all known to be 2/5(m)(r^2) I calculate this in 2 ways. One by triple integration and one by disk method. From the textbooks, moment of inertia should be in the form, dI = (r^2) dm, However, the textbook, University...
  8. CivilSigma

    Moments of Inertia by Integration

    Homework Statement I am having trouble understanding the formula for Moments Of Inertia by direct integration. Homework Equations I understand the following (which is the definition) : $$ I_x = \int y^2 dA $$ $$I_y = \int x^2 dA $$ However come to application on a problem, my book doesn't...
  9. L

    Qualitative question about inertia and gravity

    Homework Statement Why does an object with a bigger mass(more inertia) accelerate the same as an object with a lesser mass(less inertia) when in free fall? Homework EquationsThe Attempt at a Solution
  10. I

    Calculating Inertia in 3D: What You Need to Know

    Hi! is there anyway to calculate inertia in 3d? for all forms, like we do in 2d, is it the same? https://upload.wikimedia.org/math/d/d/3/dd3b5877d05c86142f03703ac1c6562b.png
  11. C

    Identical Hollow and Solid Spheres

    Homework Statement Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which. Homework Equations mgh= ½ m v^2 + ½ I ω^2 where I= 2/3 mr2 for a hollow sphere I=2/5 mr2 for a solid sphere The Attempt...
  12. B

    Setting up a Double Integral for Moment of Inertia

    Homework Statement >Problem:<br>Find the Moment of Inertia of a circular disk of uniform density about an axis which passes through the center and makes an angle of $\dfrac{\pi}{6}$ with the plane of the disc. Homework Equations Moment of Inertia ($I$) is $$\int r^2dm$$ where $r$ is the...
  13. T

    I Would Gravity Exist Without Inertia?

    Hello, Let me explain my question. We know from GR, that gravity is just something (planet, light, etc) following a geodesic path through distorted spacetime. But that's just because everything is still in motion from the big bang, traveling at the speed of its own inertia. So let's assume...
  14. 24forChromium

    Moment of inertia of a cylinder in unusual position

    See image. It would be better if you can show me the calculation process. EDIT: the axis of rotation goes right through the centre of the cylinder. NEVER MIND! GOT IT!
  15. J

    Moment of Inertia of multiple bodies in contact

    What is the overall moment of inertia of many cylinders in contact, where each is rotated about an axis through its center of mass. For example, a set of rollers. (See picture)
  16. Z

    Different formulae for moment of inertia

    I know the formula for moment of inertia is but there are I = MR^2 but there are also formulae for different objects as shown in the picture. So, how and when do you use I = MR^2 ? Just in case of (a)? Thanks!
  17. A

    Moment of inertia about tangent of a hoop

    The hoop has radius R. I used the same way to plot the axis for the hoop: ##l^2 = r^2= 4R^2cos\theta## since: ##r=2Rcos\theta## 2\rho \int_{0}^{\frac{\pi}{2}} r^2 r d\theta 2\rho \int_{0}^{\frac{\pi}{2}} 8R^3 cos^3\theta d\theta answer is \frac{32}{3}R^3\rho , and its wrong using the...
  18. amjad-sh

    Rotational inertia: a contradiction?

    We know that the rotational inertia I of a certain object is I =∫r∧2 dm where r is the distance between the axis of rotation and the increment of this object that carries a mass dm. What confuses here is the following: Take for example a hoop of mass M and radius R. Integration theory gives...
  19. O

    Physics Experiment Help (Torque, Angular Momentum, etc)

    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Hey, So I am not sure if this is in the right section but feel free to move it. We are conducting an experiment at school at the moment and are having difficulty understanding all the theory...
  20. S

    Net Angular Momentum of Satellite with Reaction Wheel

    I am modelling the attitude dynamics of a satellite. The satellite has a reaction wheel in 1 plane to help control the attitude. There is significant debate about the equation for the net angular momentum of the satellite and what inertia tensors should be used regarding parallel axis theorems...
  21. M

    Is my procedure correct to compute this moment of inertia J?

    Looking at the image below, we have the function z^2=\frac{r^2}{a} yrevolving about y-axis. We know that y goes from 0 to "a". We also know the mass of the object (of uniform density). Do you think is my procedure correct? Do you get the same result?
  22. L

    Why Are There Different Units for Moment of Inertia?

    Hi, I am a bit confused about the units of MI...I read that MI of rectangle is b*d^3/12,so unit is mm^4..Also i read in wiki that unit of MI is kg.mm^2... Both are correct,but why this difference is?
  23. S

    Moment of inertia (formula problem)

    1. Material 2. Questions: a) (pink) Why does the author use two different values of inertia for the same slender rod ? The Attempt at a Solution [/B] a) I could assume that 1/3 is holding it at the end and 1/12 is holding it in the center. But it's not interchangeable because if I chose 1/3...
  24. J-dizzal

    Pulley problem, acceleration, angular velocity, inertia

    Homework Statement In the figure, block 1 has mass m1 = 450 g, block 2 has mass m2 = 530 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.3 cm. When released from rest, block 2 falls 71 cm in 5.0 s without the cord slipping on the pulley. (a) What is the magnitude of...
  25. K

    Moment of inertia of a non-homogenous cylinder

    Homework Statement What is the moment of inertia round the axis of a cylinder length L, mass M and a linear distribution of mass with the radius R, zero at the center. Homework Equations Moment of inertia: ##I=mr^2#3 The Attempt at a Solution The density ρ=kr. what is k? the total mass is M...
  26. K

    Moments of inertia of a rectangular plate

    Homework Statement Show that the moment of inertia of a rectangular plate round it's diagonal, line B-B is equal to the one round a line parallel to one of the edges and passing through the center, line C-C Homework Equations Moment of inertia: ##I=mr^2## The Attempt at a Solution For the...
  27. K

    How Do You Calculate the Moment of Inertia for Different Axes in a Cube?

    Homework Statement Calculate the moment of inertia of a cube of mass M and edges d round an axiz, z, that passes in the middle. Then calculate around an axis parallel to the z axis and passing on one of the edges Homework Equations Moment of inertia: ##I=\int r^2dm## The Attempt at a...
  28. Q

    Does weight / inertia / momentum change with temperature?

    I did a simple experiment. I took a small block of copper (40g) and sensitive scales. First I cooled the block in a freezer (-2C) and checked its weight. Then heated it up to 300C in the oven and checked weight again. The difference in weight is well observed (4 - 5mg). Results are consistent...
  29. rpthomps

    Rotational Inertia of a triangle

    Homework Statement A thin, uniform vane of mass M is in the shape of a right triangle, as shown. Find the rotational inertia about a vertical axis through its apex, as shown in the figure. Express your answer in terms of the triangle’s base width b and its mass M. Homework EquationsThe...
  30. jdawg

    Moments of Inertia for Composite Area

    Homework Statement Determine the moment of inertia of the cross sectional area of the T beam with respect to the x' axis passing through the centroid of the cross section.(I'm attaching a diagram) Homework EquationsThe Attempt at a Solution Hi! I'm having a little trouble with this problem...
  31. M

    Moment of inertia and the geometric center

    Homework Statement The profiled steel I above is topped by a " profiled C ". Determine the moments of inertia of the structure composed by the axes central x and y through its geometric center C. Picture representing the problem: Homework Equations Profiled C and I information: The Attempt...
  32. TenPin

    Momentum, Inertia, and Deflection

    Hi, new here, so I hope I'm doing this correctly. I'll keep this question as brief as possible, but it requires just a bit of setup. I'm not an engineer or physicist, but do have a more than decent layman's understanding. I've lately become fixated on the game of bowling (ten pin), and have...
  33. 24forChromium

    Calculating the Angular Inertia of a Disk without Calculus

    Homework Statement What is the angular inertia of a disk (cylinder) with... Maximal radius, rmax = 10cm Thickness, h = 4cm density, d = 3g/cm3 rotational axis in its centre (like the axis of clock hand in a disk shaped clock) Please show and explain your procedure in finding the...
  34. **Mariam**

    Moment of inertia from diffrent axis

    Homework Statement Two particles of mass m1 = 14 kg and m2 = 24 kg are connected by a massless rod of length 1.4 m. Find the moment of inertia of this system for rotations about the following pivot points. Assume the rotation axis is perpendicular to the rod. A) center of rod B) end of m1...
  35. Deepak K Kapur

    Is Inertia a Universal Force of Resistance?

    Force is something that causes acceleration... Inertia is something that opposes acceleration...Can inertia be understood as some kind of negative force prevelant everywhere in the universe? (Hope this doesn't get locked/deleted, these days one can't even think safely)
  36. j3dwards

    Moment of inertia of ring with 3 masses on

    Homework Statement Three particles, each with mass m = 0.5 kg, are fixed on a uniform circular ring of mass M = 2 kg, radius a = 0.6 m and centre O, to form the corners of an equilateral triangle. What is the moment of inertia of this system? Homework Equations I = Σma2 The Attempt at a...
  37. anchonee

    Finding the product moment of inertia of this cylinder

    So the following question is attached (There is another thread with the same question but no solution to what I am asking on there) Now according to several solutions, apparently IYZ is equal to 0, and they reason this by saying that the geometry is symmetrical. However when looking at the...
  38. SpiderET

    Why is inertia not stopping acceleration?

    Inertia is the resistance of any physical object to any change in its state of motion, including changes to its speed and direction. It is kind of counterforce which is resisting the change of speed. But when there is this counterforce which is at the same level as force causing the...
  39. R

    Moment of inertia of rod about an axis inclined

    Homework Statement What is the Moment of inertia of rod about an axis inclined? It is given as ## \frac{ML^2sin^2θ}{12} ## but how? Homework Equations I know MOI for axis passing through center along y-axis as ## \frac{ML^2}{12} ## The Attempt at a Solution Shouldn't it be ## \frac{ML^2}{12}...
  40. T

    Moment of Inertia of a Sphere derivation?

    Hi, Is there a way to derive the moment of inertia of a sphere without using the M of I of a cylinder? In other words, is it possible to find a sphere's from scratch? Please include a derivation in your answer, unless there isn't one of course.
  41. K

    Effect of golf shaft length and flex

    Hi, I'm wondering about the effect of the shaft flex on the impact velocity between the club and the ball. I understand that as I swing down the golf club, the shaft flexes and the club head lags behind. Near the end of the point of impact, the shaft bends forward. Intuitively, I would think...
  42. bagofbones

    Moment of Inertia: Is it an Unambiguous Body Inertness Characteristic?

    I have a question about body inertness. Is moment of inertia is unambiguous inertness characteristic?
  43. ChiHawksFan

    Moment of Inertia of a Disk and Pulley System

    Homework Statement Hi all, I just had a quick question regarding a problem that I have to write a lab report on. The problem involves solving for the moment of inertia of a system that involves a pulley with a hanging mass attached to a spool that turns a flywheel. The solution is supposed to...
  44. Yam

    Concept of Moment of Inertia and its limits of integration

    Homework Statement I am trying to work the moment of inertia for a) rotating rod, axis through the centre of the rod http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3 b) Solid cylinder http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2 [/B] Homework Equations I = R^2 dM The...
  45. L

    Inertia of a Body: Explaining the Impact on Falling Passengers

    I would appreciate someone's advice on the following question: "An airplane was moving in the forward direction on the runway when it suddenly stopped. When the airplane stopped, some passengers who did not put on their seat belts fell forward from their seats. Would a passenger of larger...
  46. goonking

    Calculating Rotational Inertia: Hoops vs. Solid Cylinders

    Homework Statement Homework EquationsThe Attempt at a Solution I assume the energy stored is = 1/2 (I) (ω^2) I (moment of inertia) is MR^2 since it's a hoop? or is it a solid cylinder? do we need to convert the rpm (revolutions per minute) to radians per sec?
  47. B

    Relationship between inverse matrix and inertia tensor?

    Seems exist some relationship between the inverse of a matrix with the inertia tensor, looks: This relationship really exist?
  48. trytodoit

    How to derive the formula for moment of inertia of polygon?

    Sorry to bring this question up again. @aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as: $$...
  49. D

    Rotational Inertia of a Pulley System

    Homework Statement Homework Equations Kinetic Energy = 0.5 I w^2 v = r * w torque = Inertia * angular acceleration The Attempt at a Solution That's the problem. I have no idea where to start. I assume that the end goal is to find the angular velocity, and convert to linear velocity, but I...
Back
Top