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. R

    Rotational Inertia about Rotation Axis Through COM

    Homework Statement A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the...
  2. W

    Understanding Moment of Inertia for a Beam Bending about the Y-Axis

    Homework Statement I'm supposed to solve for the maximum moment assuming the beam bends about the y-axis (not the z axis as shown in the image. Same image for different questions). I don't understand how to find the moment of inertia in this case. The solution gives the moment of inertia for...
  3. KiNGGeexD

    Moment of inertia of circular flywheel

    Hi I'm new to this forum so still getting used to it! I have to find the moment of inertia of a circular flywheel which has radius, a and mass m! But also had area density (mass per unit area) of ρ0, Where ρ0=ρa(1+r/a) I know moment of inertia is the integral of a^2 dm and in order to...
  4. J

    Rotational Inertia: Calculate & Plot Function w/ Sinus Decay

    Hi, I would like to calculate the function of a rotating disc that has 2 spring slowing it down. (look at my pictures to understand) Let say I turn my disc 90 degrees clockwise and release it, it is going to oscillate a certain moment than stop. I want to plot that function and to have a...
  5. L

    Calculating Rotational Inertia (A Bit of Confusion)

    Hey all, Perhaps this is a bit stupid... I'm familiar with the normal procedure of calculating rotational inertia (using integration, parallel axis theorem, etc.). However, I had a confusing thought: if the center of mass of a body is the point at which you can treat as all of the mass being...
  6. S

    Moment of inertia of a cylinder about perpendicular axes

    Homework Statement Calculate the moment of inertia of a uniform, solid cylinder about it's perpendicular axes. The cylinder has length L, radius R, and total mass M. It is centered on the origin with the z-axis running through the center of it's circular faces. Homework Equations I =...
  7. S

    Classical Mechanics-Moments of Inertia and Torques

    Homework Statement a)Two people are holding the ends of a plank of length l and mass M. Show that, if one suddenly let's go, the initial acceleration of the free end (aD) is 3g/2. (7 marks). Moment of inertia, I, of the plank about its centre of mass is given by I=1/12(Ml2) b)Show...
  8. A

    Moment of inertia lab graph reading assistance

    The problem I am currently trying to right a lab report on a experiment trying to find a flywheels moment of inertia. In the lab we had a fly wheel connected to a mass on a string, and measured the position of a point on the wheel as the mass was accelerating downwards. The data was analysed...
  9. F

    Question about inertia and acceleration

    This question is just about a thought I was having. If a 1 kg object which is at rest is made to accelerate with a force of 20 Newtons and then three seconds later have an opposing force of 20 N applied to it with an impulse of (1)60/(T=0), would the object begin to accelerate in the opposite...
  10. N

    Moment of inertia of a spherical shell

    Hey. There's one thing I've always been wondering about when it comes to deriving the expression for the moment of inertia of a spherical shell. Namely, why is the length of the infinitesimal cylinder used in the derivations (like here ) equal to ##R d \theta##, instead of ##R d \theta...
  11. P

    How Does Mass Distribution Affect Rotational Dynamics of a Rod?

    Homework Statement A rod of mass M and length l rotates in a vertical plane about its centre which is on a frictionless, horizontal pivot. On the ends of the rod are point-like masses m1 and m2, where m1 != m2. a)moment of inerta about the center of the rod b)Determine the angular momentum...
  12. G

    Center of gravity & moment of inertia

    Dear forum, while standing, spreading your legs helps your stability because you have a wider base. but doesn't spreading your legs lowers your center of gravity, thus shortening the distance (r) from your center of gravity to the ground, and therefore lowering your moment of inertia = making...
  13. P

    Calculate the moment of inertia of an object

    So we just learned about moment of inertia in my first year physics class, and how to calculate it. Though I do know how to calculate the moment of inertia of an object, I don't really know what it is. I tried looking on wikipedia and the explanations just seem to be equations. What exactly is...
  14. D

    Moment of Inertia (Triangular Prism)

    Homework Statement A triangular prism (like a box of toblerone) of mass M, whose ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z axis. Find its moment of inertia for rotation about the z axis. Without doing any...
  15. M

    Derivation for Moment of Inertia of Rectangle rotated through center

    Homework Statement I need to know how to derive the equation for the moment of inertia of a rectangle rotated about an axis through its center. The rectangle has sides a and b. I know the equation to be (1/12)M(a2+b2), but I am having trouble deriving it. I have searched all over the...
  16. U

    Calculating Inertia and Kinetic Energy of Connected Shafts

    Homework Statement b) During the operation of a machine, two shafts rotate in opposite directions and are then connected by a clutch system. Shaft 1 has a rotational speed of 800 rev/min, a mass of 35 kg and a radius of gyration of 375 mm. Shaft 2 has a rotational speed of 1100 rev/min, a...
  17. J

    How to Calculate Moment of Inertia for a Disk Using Calculus?

    I know that the moment of inertia of a disk about the axis perpendicular to the plane of the disk is I=1/2 MR^2 and by the perpendicular axis theorem the moment of inertia about the other axis is I=1/4 MR^2 I want to get the 2nd result with calculus. I can't get the right answer...
  18. M

    What factors affect the movement of a ball bearing attached to a spinning disc?

    Hello everyone, Being new here, and not a "Physics Guy" I wasn't sure where this should go, but General Physics seemed like the best bet. Recently I've been thinking about the effects of circular motion on external objects, and I've hit dead end with one of my trains of thought. Excuse...
  19. R

    Moment of Inertia of a molecule of collinear atoms

    Homework Statement Landau&Lifshitz Vol. Mechanics, p101 Q1Find the moment of inertia of a molecule of collinear atoms Homework Equations The Attempt at a Solution I defined the origin alone the orientation of the molecule. I_3=0 obviously. For I_2 I wrote I_2=Ʃm_b[x_b-\frac{Ʃm_a x_a}{μ}]^2...
  20. C

    Dynamics question regarding moment of inertia

    Hi, I have a question regarding a dynamics question that be found here:http://by.genie.uottawa.ca/~mess/files/MCG_2107/MCG2107_M2005_p2.pdf, It is the first problem on that link (labeled number 2.) I did ƩFx, ƩFy, ƩMG which allowed me to find angular acceleration, frictional force, and...
  21. P

    Moment of Inertia of a Rectangle

    I have been trying to do the moment of inertia of a rectangle and I have it figured out when we have the center of the rectangle as the center of the rotation. The equation is ∫∫ρ(x^2+y^2)dy dx where the first integral is from -b/2 to b/2 (if b is the height) and the second integral is -a/2 to...
  22. J

    Pulleys with inertia and friction

    Homework Statement http://essbaum.com/images/Pulley_diagram.png We have a bonus question where we are asked to find the mass of ##m_{1}## necessary to accelerate ##m_{2}## upward at ##1g##, and we have to include friction in the pulley bearings as well as the pulley inertias. The...
  23. L

    Finding the moment of inertia of a neutron star

    Homework Statement The Crab Nebula is a cloud of glowing gas about 10 light-years across, located about 6500 light years from the Earth (the figure (Figure 1) ). It is the remnant of a star that underwent a supernova explosion, seen on Earth in 1054 a.d. Energy is released by the Crab Nebula...
  24. PhysicsKid0123

    Sphere vs Cube: Rotational Inertia

    Which would have more rotational inertia? A sphere or cube? Suppose they have the same mass, the side of the cube has the same length as the diameter of the sphere, the cube's rotation axis is perpendicular to two of its faces. Which one would have more rotational inertia about an axis through...
  25. G

    Expressing moment of inertia in terms of m,a,r and g

    Homework Statement Find an expression for the moment of inertia (I) of the platform in terms of acceleration of the mass (a), the value of the hanging mass (m), the radius of the spindle (r) and the constant (g). Diagram: http://i.imgur.com/rv3zFYG.jpg Homework Equations F=ma t=Iα...
  26. F

    Inertia - Moments of Inertia of a rigid body (different axes)

    Inertia -- Moments of Inertia of a rigid body (different axes) Here is the problem http://imgur.com/pL6Bdgw So I missed class today because I was studying for a genetics test. I don't need the answer or anything but I was wondering what the general rule for inertia that I would use for...
  27. S

    MHB Indexes of inertia for the function

    Hello everyone Here is the question Find positive and negative indexes of inertia for the function $q(x)=TrX^2$ on the space $M_n(R)$ I did some work, first I suppose $X$ as a n by n matrix, then $TrX^2=a_{11}^2 +...+a_{nn}^2+2(a_{ij}a_{ji})$ It seems like that all terms are positive...
  28. J

    Moment of Inertia of Curves and Surfaces

    Greetings! I enjoyed the definition of moment of inertia for a volume and for an area in the form of matrix. It's very enlightening! I = \int \begin{bmatrix} y^2+z^2 & -xy & -xz\\ -yx & x^2+z^2 & -yz\\ -zx & -zy & x^2+y^2 \end{bmatrix}dxdydz '->...
  29. S

    Torque and Moment of Inertia of a black ring

    Homework Statement A black ring is placed concentrically on a turntable and is being pulled by a constant force of 12.5 N and the force is applied at a distance of .01m from the spindle/pulley. It's known that the ring accounts for about 8.50% of the total moment of inertia. Find moment of...
  30. L

    How Is Angular Speed Calculated in a Dual Disk System with a Falling Mass?

    Homework Statement A block of mass m = 4 kg hangs from a rope that is wrapped around a disk of mass m and radius R1 = 27 cm. This disk is glued onto another disk of again the same mass m and radius R2 = 66 cm. The two disks rotate on a fixed axle without friction. If the block is released at a...
  31. X

    Understanding Rotational Inertia: A Homework Challenge

    Homework Statement in Attachment Homework Equations I = .5*mr^2 The Attempt at a Solution I have no idea what is going on. This is a pre section quiz and I guessed on one and got it right. I don't know what is meant by the equations not giving I. I googled and noticed I has...
  32. C

    Why Does the Calculation of Moment of Inertia Differ in This Problem?

    Hi friends the problem is as: https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-ash4/1379445_1440214886205617_1276077735_n.jpg While finding moment of inertia of the system about the point from where the rod is fixed, the book says that M.I. of the system will be, I = Irod + Idisc I =...
  33. K

    Moment of Inertia confusion

    Homework Statement Small blocks, each with mass m, are clamped at the ends and at the center of a rod of length L and negligible mass Compute the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end...
  34. W

    Moment of Inertia Using Parallel Axis Theorem

    Homework Statement Q is the edge length of the cube. The moment of inertia of the cube about an axis passing through its center and the center of two opposing faces is (1/6)mQ^2 (PCM in the diagram). Use the parallel axis theorem to find the moment of inertia if the axis is along one face of...
  35. F

    Understanding constant velocity, inertia and rest

    I've come to the conclusion that i don't understand at all the concept behind inertia. How can we know when an object stays at rest or at constant velocity? (take for example a girl in a rope. She would tighten her grip on the rope until the tension balances the force of gravity (assume rope is...
  36. S

    Heavier object has higher inertia

    I learn that inertia means the tendency an object will remain from changes. Heavier object has higher inertia, which means higher tendency to resist change. So, here is an example from my teacher. A car accelerates, the driver is pulled backward and hit the rear of his seat. This is due to...
  37. U

    Torque, rotational inertia and angular acceleartion

    Homework Statement In order to link these into a logical sequence, how do they fit together Homework Equations I = rotational inertia a = angular acceleration (I know a different symbol is usually used) τ= force x moment arm distance The Attempt at a Solution so...to...
  38. M

    Inertia forces in an ic engine

    when they say the inertia forces in the engine,what does it refer to ? this is with respect to the fact that in a diesel engine the point of maximum pressure is at combustion as there are no sufficient inertia forces to cancel out load forces..
  39. D

    Why is the inertia tensor calculated about a point instead of an axis?

    Generally, when we talk about moment of inertia, we talk about rotation and inherently, we talk about moment of inertia about an axis. But when we talk about inertia tensor, we calculate about a point. Is there a reason for this difference? Am I missing something? I am new to tensors.
  40. M

    What is the Polar Moment of Inertia and How is it Calculated?

    I know some of you may have given up on me understanding moment of inertia/second moment of area, but here is another problem. I am using the this table to get the equations for the polar moment of area of a hemicircle around the x-axis, then I am applying the parallel axis theorem to find the...
  41. M

    Moment of inertia with T shape

    ]1. Homework Statement [/b] Homework Equations The Attempt at a Solution On paper it looks like not much of an attempt has been made, but I have tried a few different ways to find I_y. I thought to take the entire rectangle and subtract the parts on the upper left and right...
  42. Q

    Can We Slow Down an Object's Inertia to See It Age Faster Than Us?

    Hi PF, I am trying to get a good explanation regarding time dilation and how it works. I want to understand why we can't slow an objects inertia down enough to see it age faster than we age at our velocity. I will try to use a reference which is understandable to everyone. So, an easy...
  43. C

    General: Calculating the Moment of Inertia

    Hey, sorry for not using the exact template; I just have a general question about how to calculate the moment of inertia that I will have to apply to a number of instances. In this particular case, I need to calculate the moment of inertia for a rod pendulum. Of course, I could just use...
  44. G

    Moment of inertia of a point mass

    Hello, This is a very basic question. Wikipedia says moment of inertia I of a point mass m is calculated as: I = m * r^2 Where, r is distance from the axis of rotation. What this actually mean? I mean what is an r?
  45. G

    How to find the moment of inertia of a cube?

    Hello, If I have a rigid cube rotated about an axis with dimensions L x W x H centimeters, how can we find the moment of inertia? Thank you.
  46. S

    Moment inertia - theoretical problem

    Moment inertia -- theoretical problem Homework Statement Show that the moment inertia of a hollow cylinder with inner radius a and outer radius b is (1/2)*M*(a^2+b^2), calculated for the center axis. Homework Equations I know that the moment inertia of a non-hollow cylinder is I =...
  47. I

    Increase moment of inertia, slipping down an incline

    Hi, I'm trying to find out what effect an increase in moment of inertia of a cylinder would have on slipping when the cylinder rolls down an incline. Starting with: ma=mgsin(theta)-f, where f is the friction force, which is less than or equal to µmgcos(theta), normal force times µ. We already...
  48. M

    Increased mass (inertia) affect on wind drag

    Okay, so the scenario is a passenger car, traveling on the highway. As a general rule, I say that increased weight (mass) will have a beneficial effect on MPG (IF tire pressure is increased so that rolling resistance is reduced to compensate for the increased weight), ONCE the vehicle is up to...
  49. PsychonautQQ

    Moment of Inertia of mud thrown on door

    Homework Statement A solid wood door 1m wide and 2m high is hinged along one side and has a total mass of 40kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass .5kg. What is the original and final moment of inertia for the door? What is the...
  50. O

    The moment of inertia of a rectangular plate about its diagonal

    Homework Statement Find the moment of inertia of a rectangular plate of mass m, sides 2h and 2k , rotates about its diagonal. Homework Equations I= Ʃmr^2 The Attempt at a Solution I=Ʃ m(x^2 +y^2) , let 2h parallel to x-axis, 2k parallel to y-axis. I= m(x cosθ)^2 + m (y cos ∅)^2 where...
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