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. L

    Inertia tensor combination point mass-sphere

    Homework Statement hello, i want to calculate the inertia tensor of the combination of a point mass and a sphere in the object's frame, the center of mass is at the origin. The point mass remains at the surface of the phere The sphere is uniform, radius r and mass M, and the point mass has mass...
  2. F

    Do We Agree on How Orbits Work?

    Would you guys agree with these websites on how orbits work? http://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-orbit-58.htmlhttp://www.qrg.northwestern.edu/projects/vss/docs/space-environment/1-what-causes-an-orbit.html
  3. F

    Momentum vs Inertia: Is Momentum a Measure of Resistance?

    Hi. So I know that inertia (the resistance of an object to a change in its velocity) is reliant on mass. I also know that momentum is mass times velocity. So momentum is really inertia times velocity. My question is: if that's so, is momentum then not a measure of a moving object's inertia, its...
  4. S

    Rotational Inertia, Torque and Angular Acceleration (1Q)

    Homework Statement . What is the angular acceleration if a force of 3 N is applied perpendicular to the radius of a 5 kg solid sphere that has a radius of 0.6 meters? Homework Equations = r x F I = mr^2 The Attempt at a Solution I used tried solving for angular acce. 3N/(5kg)(0.6)...
  5. P

    Inertial Frame of Reference vs Spacetime

    Is the inertial frame of reference the same thing as space time?
  6. J

    Derivation of moment of inertia of a solid sphere

    Homework Statement I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks The Attempt at a Solution I am attempting...
  7. A

    How to Calculate the Moment of Inertia for a Half Disk System?

    in this video http://www.physicsgalaxy.com/lectures/1/44/234/Solved-Example-2#12(see only the question) the method illustrated is integration but i thought of an alternate method, moment of inertia of half disc with radius r2 is 1/2mr2^2 and that of half disc with radius r1 is 1/2mr1^2.so...
  8. David Earnsure

    Different diameter rotational inertia

    Homework Statement I am doing the old frozen can vs liquid can experiment and one of the questions asks that if cans with different diameters were used with the same contents (so same mass relative to diameter size) how would this effect the time taken for the cans to go down a ramp (how would...
  9. Arman777

    Moment of Inertia of Half Ring (Half Circle)

    Homework Statement Theres an object which makes a pendulum motion.Lets suppose we hang the mass to the ceiling.We released the object with inital angle 0 to the ceiling.(I mean the angle between the object and the ceiling is zero).Whats the moment of the Inertia to the point A. A is a...
  10. dumbdumNotSmart

    Angular acceleration in moment of inertia

    I'm having a hard time undertanding a concept of moment of inertia and Angular acceleration. Homework Statement We have a closed system above. M1 is a cylinder of 2 Kilograms, moment of inertia of a cylinder ( MR2 /2 ) with a string tightly rolled around it. This string connects to a free...
  11. NinjaChachi

    Physics Lab Help - Moment of inertia and acceleration

    Homework Statement In our physics lab we were to set up a system looking like this: where the mass was released and the velocity/acceleration and of the ring was calculated using MotionLab software. Our goal was to find the predicted total moment of inertia by just calculating the moment of...
  12. vetgirl1990

    Moment of inertia for composite objects

    Homework Statement Find the moment of inertia of these composite objects. I've attached two different composite objects; each rod has length L and mass M. Homework Equations I = Icm + MD2 Long thin rod with rotation axis through centre: Icm = 1/12ML2 Long thin rod with rotation axis through...
  13. I

    Moment of inertia of a cylinder

    Homework Statement Need to find the moment of inertia of a cylinder, about its center of mass, about the three principle axes. Z axis is normal to the circular faces of the cylinder. mass = M, radius = R, height = h Homework Equations ∑miri2 The Attempt at a Solution The Izz for whatever...
  14. vetgirl1990

    Moment of inertia for composite object

    Homework Statement Find the moment of inertia for this composite object: M1=5kg at (3,4) and M2=3kg at (6,8) Homework Equations Moment if inertia for point particle = MR2 The Attempt at a Solution I'm not sure if moment of inertia should be componentized -- broken up into x and y...
  15. A

    Difference between Rotation Inertia of Rod V.S Cylinder

    A rod and Cylinder with a same axis of rotation relative to its body have different rotational inertia equation. WHY? Thanks in advanced.
  16. T

    How can the moment of inertia of an object be calculated on an arbitrary axis?

    This seems to be a crucial detail that I just glossed over, but when finding the inertia tensor of an object, is the origin always situated at the object centre of mass? For example: In the link (http://hepweb.ucsd.edu/ph110b/110b_notes/node26.html ), is it necessary to do the integral from...
  17. W

    Finding second moment of inertia about x axis

    Homework Statement The cubic is divided into 4 parts , A, B and C, D , each with thickness of 1mm , i am sked to find thesecond moment of inertia about x -axis Homework EquationsThe Attempt at a Solution i' m using the formula Ixx = Ix +A(d^2)[/B] for part CD, Ixx = 50(1^3) / 12 + 50...
  18. vetgirl1990

    Applying the parallel axis theorem to find inertia

    Homework Statement Calculate the moment of inertia of a uniform rigid rod of length L and mass M, about an axis perpendicular to the rod through one end. Homework Equations Parallel axis theorem: I = Icm + MD2 Long thin rod with rotation axis through centre: Icm = 1/12 ML2 Long thin rod with...
  19. A

    Why do Jet fighter pilots experience a greater G-force?

    Hi! I'm a high school student, aspiring to pursue a career in Astronautical Engineering. I always try and ponder on questions about everyday aerodynamics and physics. So, here's a question from you from an aspiring scholar. It is known that, at high velocities, pilots in super-sonic jet...
  20. M

    Moment of Inertia: Disk 1 & 2 Homework

    Homework Statement In the diagram, Disk 1 has a moment of inertia of 4.40 kg · m2 and is rotating in the counterclockwise direction with an angular speed of 7.50 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 9.50 rad/s falls...
  21. jcruise322

    Question regarding block and pulley system with inertia

    This problem is an example from Mosca and Tipler, 9-13, 6th edition. I believe the books equation for the acceleration of the system is incorrect according to my work... Anyway, here goes 1. Homework Statement "Two blocks are connected by a string that passes over a disk pulley of radius R...
  22. tshah321

    Moment of inertia about center of mass with four holes?

    Homework Statement What is the moment of inertia of the 4 kg disk below when it rotates about the center of mass? The mass of the disk without the holes is 6 kg . Homework Equations Center of mass equation: (1/M)(∫xdm) Moment of inertia of a disk: I = 0.5mr2 Parallel axis theorem: I = Io +...
  23. R

    Total Moment of Inertia of Two Rods

    Homework Statement The rods of length 2 meters and and mass 20 kg are joined at their ends to form a V shape. What is the total moment of inertia measured from the reference point perpendicular to the plane of the paper and at the point where the two rods are joined. (So find total moment of...
  24. CentrifugalKing

    Two Toilet Papers dropping-Rotational Inertia

    Homework Statement Okay, so I'm supposed to take two fresh rolls of toilet paper and drop them. One of which, I am supposed to let unravel while falling. The other, I just drop on its own. I'm supposed to find the height at which both will drop and hit the ground at the same time. Homework...
  25. C

    Finding moment of inertia of irregular object with calculus?

    For a mathematics project I'm trying to figure out the moment of inertia for a propeller. I'm told that it is possible to find the moment of inertia of irregular objects through calculus, so I'm determined to figure it out using calculus. I plan on using a 3D modelling program (since I don't...
  26. A

    How do you find linear density given mass per kg?

    Homework Statement I need to find the final impact speed of the flame of a non-uniform candle. I am given that the mass per unit length increases linearly from top to bottom starting with 1kg/m at the bottom and 10kg/m at the top. I need to find how fast the candle flame is moving once the...
  27. B

    Understanding Moments of Inertia: A Guide for Solving Homework Problems

    Homework Statement Attached in a picture! Homework Equations I = mr^2 m = (x*y) cm = (x/2, y/2) The Attempt at a Solution I was able to solve Part 1 fairly fast, but Part II has drawn a blank for me overall. I was thinking of that rotational thing from Calculus where you spin a 2D figure...
  28. ognik

    MHB Inertia matrix from orbital angular momentum of the ith element (please check)

    Starting with the orbital angular momentum of the ith element of mass, $ \vec{L}_I = \vec{r}_I \times \vec{p}_I = m_i \vec{r}_i \times \left( \omega \times \vec{r}_i\right) $, derive the inertia matrix such that $\vec{L} =I\omega, |\vec{L} \rangle = I |\vec{\omega} \rangle $ I used a X b X c...
  29. S

    Calculating Moment of Inertia Homework: Soccer Ball

    Homework Statement An object rolls down a ramp starting from rest, demonstrate symbolically the calculation needed to go from time given to a measured κ value here. Pick your favourite object and perform the calculation. d, m, R, t, h are known http://puu.sh/luare/10352d0479.png Soccer Ball...
  30. A

    Increasing speed by decreasing intertia?

    Just curious, explanation if youre going to answer please! 2 horizontal disks stacked on one another spinning at constant v, (about a frictionless axis perpendicular to their center), both have mass. Okay, so let's say its possible to instantaneously remove the top disk. So would that make...
  31. A

    Moment of Inertia of Rod About Axis XX': ML2/3sin2α

    1. The problem statementα, all variables and given/known data The moment of inertia of a Rod over an Axis XX' passing through the center of mass of the Rod at an angle α is- Homework Equations Moment of Inertia of Rod about the end, I =ML2/3 The Attempt at a Solution I=ML2/3 Answer of the...
  32. C

    Where can I start learning about moments of inertia?

    Homework Statement My question doesn't follow the guidelines for asking for homework help because I'm looking for sources where I can learn about moments of inertia, not help for a specific homework problem. I'm going to try to figure out the moment of inertia of a propeller, but I don't know...
  33. dumbdumNotSmart

    What is the acceleration of a cylinder when a torque is applied to it?

    Homework Statement Got a spicy one for you today. There is a cylinder of mass 5kg (M) with no angular velocity and no velocity, on a surface of static friction constant μ=0.6 . It's radius is .1 meters (R). Its baricentric moment of inertia is characterized by I=.5MR^2 . Gravity is 10m/s...
  34. shanepitts

    Finding the angular momentum using the inertia tensor/matrix

    Homework Statement A thin ring of radius r is constrained to rotate with constant angular velocity ω as shown in attached picture. Let the linear mass density of the ring be ρ(θ)=ρ0(2+sin2θ) where ρ0 is constant. a) Find the angular momentum L of the ring about O, at the instant the ring is in...
  35. C

    Why Does a Rolling Sphere Climb Higher Than a Sliding Particle?

    Homework Statement A uniform sphere and a particle are sent one-by-one with the same initial speed up the same incline. Each rises to a maximum height before falling back towards the starting point. The sphere rolls without slipping; the particle slides without friction. Use conservation of...
  36. Electro Dave

    Power needed to move a vehicle against inertia

    Hi, I'm trying to figure out the minimum power in watts or HP to move a front wheel drive vehicle that is man-powered with pedals, of a given base weight and then to know how much people would be needed to pedal in order to break inertia and a constant of how much more power is needed for each...
  37. T

    Lab experiment on moment of inertia dynamic

    Homework Statement That is the set up for experiment, and I attached the data I found in the lab. The lab given me the equation to find the moment of inertia of the cylinder Homework Equations Icyl = (2hgM_cylinder) * (1/(W_withcylinder)^2 - 1/(W_nocylinder)^2) The height is 0.9m The Attempt at...
  38. S

    How Do You Calculate the Moment of Inertia for a Tapered Tube?

    Homework Statement To calculate the moment of inertia of a cantilevered tapered tube with mid-thickness large radius RL and mid-thickness small radius RS Homework Equations The Attempt at a Solution Area of the larger end of the tube AL=2*pi*RL*t Area of the smaller end of the tube...
  39. Q

    What Is the Principal Moment of Inertia in Robotics?

    Hi! I am new at robotics, can you guys please help me what is the principal moment of inertia?? how to define the pose of axis about center of mass of my robotic link of a legged robot?? please guide me with some visual representation and also how to calculate Inertia Tensor?? I will really...
  40. L

    Beginner's Guide to Automotive Mechanics: Inertia, Energy, & Torque

    hey...this is lokesh. I am really interested in automobiles but the problem is that i am a beginner. I am just not able to apply the concepts of inertia energy and torque on engines. Can you please suggest me any e-books or links which would help me clear my basics? Please reply asap. Desperate...
  41. R

    Atwood Machine Inertia Friction and directional forces

    I have an Atwood Machine. I have an aluminium Pulley of radius 4 inch. A gym cable running over it. Not sure coefficient of friction but smooth movement. One end of rope, I attach wt. of 0.5 kg. I had to attach weight of 1 kg for acceleration to start. If I attach 2 kg, I had to attach 3.1 kg...
  42. J

    Effect of wind speed on running

    Hi guys, I'm an arts undergrad student with very little knowledge of the sort of physics I'm about to ask. I was wondering if there is a calculation to work out the differentiation between running at a particular speed say 10mph against wind coming towards you at 15mph. As well as it being on...
  43. imadrea

    How to devise moment of inertia formula of solid sphere?

    Homework Statement how to divide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M. Homework Equations I=∫r2dm 2/5 MR^2 The Attempt at a Solution https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p i try to...
  44. minimario

    Moment of Inertia of Spherical Shell

    Homework Statement Find the moment of inertia of a spherical shell (hollow) with mass M and radius R. Homework Equations ## I = \int r^2 dm ## The Attempt at a Solution This is method I use to find Moment of Inertia of solid sphere: We use circular cross sections. At some radius r...
  45. K

    Is the moment of inertia matrix a tensor?

    Homework Statement Is the moment of inertia matrix a tensor? Hint: the dyadic product of two vectors transforms according to the rule for second order tensors. I is the inertia matrix L is the angular momentum \omega is the angular velocity Homework Equations The transformation rule for a...
  46. 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?
  47. 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?
  48. 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...
  49. 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
  50. 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...
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