What is Intertia: Definition and 47 Discussions

The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. Informally, it is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K−1⋅m−3.
The volumetric heat capacity can also be expressed as the specific heat capacity (heat capacity per unit of mass, in J⋅K−1⋅kg−1) times the density of the substance (in kg/L, or g/mL).This quantity may be convenient for materials that are commonly measured by volume rather than mass, as is often the case in engineering and other technical disciplines. The volumetric heat capacity often varies with temperature, and is different for each state of matter. While the substance is undergoing a phase transition, such as melting or boiling, its volumetric heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature.
The volumetric heat capacity of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (volumetric heat capacity at constant pressure) than when is heated in a closed vessel that prevents expansion (volumetric heat capacity at constant volume).
If the amount of substance is taken to be the number of moles in the sample (as is sometimes done in chemistry), one gets the molar heat capacity (whose SI unit is joule per kelvin per mole, J⋅K−1⋅mol−1).

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  1. F

    Momentum of intertia for a dihydrogen molecule

    I don't know if the value for distance between protons given in the homework is right (##d = 74.14 pm##). Indeed, on the following link : https://brainly.in/question/7147660 , they take a distance equal to ##d = 4\times10^{-10} m##. In all cases, the same formula is applied ...
  2. M

    Moment of inertia of this body

    1. The problem statement, all variables and given/known See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis Homework Equations I=mr^2 The Attempt at a Solution I tried to get the moment of intertia of rod by integration from...
  3. O

    Virtual Intertia in Power Systems

    Hi again PF. I recently came across the term "virtual inertia" when reading about photovoltaics and power converters (DC/DC, DC/AC etc.). Article: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6953370, not sure if people are able to view the article, I have access via university library...
  4. Alistair McCheyne

    Drive line inertia and torsional effects exam question

    Hi can anyone help me with this question on inertial forces in gears? Cheers Ali :)
  5. P

    I If there are gravitons, is space not curved?

    If gravitons are proven to exist, would that mean space is not curved?
  6. 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...
  7. J

    Gravity and intertia curiosity

    If gravity pulls things towards an object, is it possible that gravity pulls the object itself towards its own center, creating inertia?
  8. J

    What is the process for finding the moment of inertia for a semicircle?

    Homework Statement Find lx and ly. The Attempt at a Solution So after countless studying of this topic, and no notes from my professor to help, I thought I had the process figured out. But this initial image is throwing me off a bit. Here's what I believe to be the right process for these...
  9. K

    Angular momentum and Quantum Number l

    The question: Consider two masses of 0.1 gm each, connected by a rigid rod of length 0.5 cm, rotating about their center of mass with an angular frequency of 800 rad/s. a.) What is the value of l corresponding to this situation? b.) What is the energy difference between adjacent l-values for the...
  10. C

    Moment of Inertia - Find Area Around Y-Axis

    This is my first time posting in this site so if I left out any information or the information needs to be formatted differently I apologize ahead of time. Homework Statement Determine the moment of inertia of the area about the y axis. The curve is represented by y2=2x, and the shaded...
  11. A

    Understanding Inertia Tensor Scaling in CAD Models - Explained

    Hi everyone, I have the following problem in my hands, which I don't know how exactly to address. Let's assume that from any CAD(Solidworks, Catia), I obtain the inertia tensor of my model (impossible to calculate by hand btw). I_full=[Ixx Ixy Ixz Ixy Iyy Iyz Ixz Iyz Izz] I...
  12. E

    Moment of Intertia of a cylinder rolling inside a cylinder

    Hi all, I just have a troublesome time wrapping my head around the concept of moment of inertia of a cylinder inside a cylinder. For example, in the attached figure The moment of inertia of the cylinder with radius 'r' around the point o, according to my understanding should be I_o = I_s+...
  13. W

    How to Calculate Time and Angular Acceleration of a Slowing Disc

    The mass of the disc is M and the radius is R. The problem states: A disc completes 44 revolutions as it slows from an angular speed of 1.5 rad/sec to a complete stop. 1)W/ acceleration constant, what times is required for it to come to rest? 2) what is the angular acceleration...
  14. N

    Area moment of intertia of a t-bar

    Homework Statement The area moment of inertia about the dashed axis is what? Homework Equations Paralell Axis theorem The Attempt at a Solution (1/12)bh³ + (1/12)hb³ + bh(h/2 + b/2)² I don't understand how I am wrong
  15. N

    Computing net Moment of Intertia

    Homework Statement An object is made from 2 solid disks: m1 = 23 kg, m2 = 39kg, and r1 = 17cm, and r2 = 33cm. The disks are connected by a thin rod of M = 11kg, L = 67cm. The object is held in a horizontal position and then let go. The object is free to rotate about a pivot through centre of...
  16. S

    Moment of intertia of a cuboid

    Simple question but I've never been through the proofs to know what I'm plugging into. Are these components of the cuboid and can they just be added together for the total moment of inertia? Thanks!
  17. S

    Rotational Intertia of a rotating Space Station

    Homework Statement Four rockets attached to a (wheel) space station exert a force of 65.5N to rotate it . The space station's angular velocity is increased at a constant acceleration of 3.63 x 10-3 rads-2. Each rocket is 11.2m away from the centre. Calculate the rotational inertia of the...
  18. L

    Why does a rotating chain become horizontal?

    Hi Homework Statement A chain rotates fast. Observation: the chain gets into a horizontal position. Why? Homework Equations L=I \omega E= \frac 1 2 I \omega² E=\frac 1 2 \frac {L²} I The Attempt at a Solution Well, I have two equations for the energy. I know that I...
  19. A

    Moment of intertia of a W figure

    Homework Statement A W figure. each of the 4 arms of the W has mass M, length L, and are at right angles. axis is in the plane of W, passing through the middle, vertically. Homework Equations i used the result I=M(L sinθ)²/3 for a rod inclined at angle θ with the axis, and axis...
  20. S

    Moment of intertia for corrugated pipes

    Hi, I am struggling to find forumula for Moment of Inertia for corrugated hollow pipes somewhat as shown in the picture. Main Pipe is made of Solid wall construction over which smaller diameter hollow plastic pipe is spairally welded. Any approximate calculations will also help. Thanks...
  21. L

    Center of mass and moment of intertia semi-circle

    Homework Statement having some major derp problems. I can't seem to remember how to find moment of inertia about the COM of and object or even finding the COM for that matter. I need it to solve a Euler Lagrange problem Can someone give me an idea on the integrals to use and in what...
  22. D

    Why Is My Calculation of the Wheel's Moment of Inertia Incorrect?

    Homework Statement i've attched a picture of the wheel, which need to calculate moment of intertia with respect to 8 rods. i've tried to use stiener rule but it's not getting the answer, moment of wheel is (m1*r^2)/2 moment of rod is (m2*r^2/3) i use the rule i total = icm + mr^2...
  23. R

    Moment of Intertia for changing COG

    Hi all, I've got a 3d object modeled in Pro/Engineer with a tail. The tail can change position to some angle theta with respect to the ground. I have created a closed form solution to determine the location of the center of gravity at any angle theta. The problem is with the moment of...
  24. C

    Emergency, derive or derivative of moment of intertia

    Homework Statement Needs to be in TODAY (yeah I know I am cutting it close!) Derive an expression for the moment of inertia of the masses at the ends of the arms in terms of l, θ and m Is the example question asking for the derivative or is it asking to use the terms above in an equation...
  25. D

    Moment of intertia for a system

    Figure 1 Homework Statement Three identical marbles are on a turntable disk of radius R. The mass of the disk is {m}_{d}. The mass of each marble is {m}_{b}. What is the moment of inertia of the disk and the marbles around an axis of rotation at the edge of the disk (the dot in Figure 1)...
  26. B

    Moment of intertia of thin disc

    Homework Statement This is not a homework question but it could be. I am trying to understand why the moment of inertia of a thin disc about its axis of rotation is 1/2 MR2. Homework Equations The rotational moment of inertia of a system of points is ^{}\summr2. The Attempt at a Solution...
  27. S

    Center of mass and Moment of Intertia

    Homework Statement The thickness of the object is 2 cm. The density of the material (pronounced row) is 7800. The angle (theta) is pi/6. The radius is .75 meters. What is the moment of inertia and the center of mass? Here is what the object looks like...
  28. F

    What is the Method for Measuring Moment of Inertia in a Yo-Yo Prototype?

    Homework Statement In testing a design for a yo-yo, an engineer begins by constructing a simple prototype--a string wound about the rim of a wooden disk. She puts an axle riding on nearly frictionless ball bearings through the axis of the wooden disk and fixes the ends of the axle. In order to...
  29. J

    Finding the moment of intertia

    Homework Statement A solid sphere of mass 2 kg and 5 m radius is in space. Find its moment of inertia.Homework Equations2 moment of inertia of a solid sphere about its diameter: \frac{2}{5}MR2, where M is the mass of the sphere and R is its radius. The Attempt at a Solution I = mr^2 = (2...
  30. S

    Moment of intertia, lagrangian, etc

    A uniform ladder of mass M and length 2L is leaning aainst a frictionless vertical wall with its feet on a frictionless horizontal floor. Initially the stationary ladder is released at an angle \theta_{0} = 60o to the floor. Assume that the gravitation field g acts vertically downward. 1)...
  31. L

    Calculating moments of intertia

    1. Find the moment of inertia I_x of particle a with respect to the x-axis (that is, if the x-axis is the axis of rotation), the moment of inertia I_y of particle a with respect to the y axis, and the moment of inertia I_z of particle a with respect to the z axis (the axis that passes through...
  32. S

    Moment of Intertia, proving Parralel axis theorum. Help please.

    Imagine we have a Equilateral triangle in the xy plane with one vertex at the origin. The triangle will be rotated about the z axis. The depth of the triangle, d, will be constant.B_r=B(r) From the picture I see that B_r=\frac{r}{h}B , V=\frac{B_rhd}{2}=\frac{Bdr}{2} First, I need to find...
  33. Z

    Rolling different masses down a hill - Intertia Question

    I have a very simple conceptual physics problem that I am looking to solve, and unfortunately I've been out of school a little too long to solve: Suppose you have a hill, and at the bottom of the hill it levels off and keeps going on. You take two marbles of different masses and roll them...
  34. Y

    Linear acceleration and moments of intertia

    Im having problems with two questions, the first is linear acceleration, A 6.00-kg cylindrical reel with a radius of 0.600 m and a frictionless axle, starts from rest and speeds up uniformly as a 4.00-kg bucket falls into a well, making a light rope unwind from the reel. The bucket starts from...
  35. K

    Moment of Inertia of Wire Shaped like Astroid: Finding MOE | Solution Attempt

    Homework Statement A wire is shaped like the astroid x=cos3(t), y=sin3(t), t[0, 2*pi] and has constant density = k. Find its moment of intertia I0 around the origin. 2. The attempt at a solution To find the MOE we must integrate k* (x2 + y2)ds along the curve. We differentiate and find...
  36. C

    Moment of Intertia of Spherical Cap?

    [SOLVED] Moment of Intertia of Spherical Cap? Homework Statement I am having some serious trouble trying to setup this problem.. Find the rotational intertia about the z axis of a spherical cap cut from the sphere x^2+y^2+z^2=4 by the horizontal plane z=1. Homework Equations...
  37. K

    Moment of intertia and net work problem

    A ballerian spins initially at 1.5rev/s when arms are extended. She then draws in her arms to her body and her moment of intertia is .88kg m^2 and her angular speed increases to 4.0rev/s. Determine the network she did to increase her angular speed? To find moment of inertia was pretty simple...
  38. malawi_glenn

    Is the Moment of Inertia Formula for a Fluid Nucleus Accurate?

    Hi! I was wondering if some here can confirm this formula given by K.S Krane in his book "Introductory Nuclear Physics", page 145, eq # 5.19 \mathscr{I} _{\text{fluid}} = \dfrac{9}{8\pi}MR^2_{avg}\beta (5.19) Moment of inertia for a ellipsodial fluid. Where \beta is the deformation...
  39. S

    What is the difference between inertia and Newton's First Law?

    I'm taking my first Physics course (it's a foreign language), and in English class we were given a piece of paper on Skating taken from an English Physics textbook. We are having problems with some expressions, such as Inertia. What the heck is inertia? Is it a law? Or an expression? (I checked...
  40. K

    Calculating Moment of Inertia for Cylinder and Sphere Intersection

    Find the moment of inertia around the x-axis of the region that lies inside both the cylinder r=a and the sphere rho=2a. *Here's what I've done so far: http://www.badongo.com/pic/574867 Am I on the right track? If so, what's the next step? If not, what's wrong?
  41. K

    Torque/moment of intertia questions

    i have two questions that i need help understanding 1a. Homework Statement A majorette takes tow batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.6m long and each ball on the end is 0.50kg. (Ignore the mass of the rods.) What is the moment...
  42. M

    What is the axis for #21 on Moment of Inertia?

    http://img100.imageshack.us/img100/1756/untitled2qx1.jpg I am having trouble with #21. I already did #20, but I have NO idea of how to do #21. First of all, I am not really sure where is the axis suppose to be.
  43. S

    Moment of intertia for rod with weight on one end

    Hello, I'm trying to derive the moment of inertia for a long rod with a point-weight on one end (the rod rotates through its midpoint). Could anyone offer any help? I know the formula for the rod is normally (1/2)ML^2, but I'm not sure how the weight on one end alters that. Thanks!
  44. G

    Calculating Inertia Tensor for Elliptical Rotation: How to Find Torque?

    I have an ellipse rotating around a fixed axis that passes through it's center, with a constant angular speed \omega. I'm being asked what torque would generate this motion. It should be \vec{\Tau} = \frac{d(I \vec{\omega})}{dt} = \dot{I} \vec{\omega} since angular speed is constant. I'm not...
  45. D

    Yet another moment of intertia problem and such

    Hello again, got some rather interesting questions for those who have been kind enough to put up with my ridiculous free response questions over the past 3 weeks. Here it goes: A solid disk (of Radius R) has four holes cut out of it, each of which are centered at R/2. The holes have a...
  46. C

    Angular speed and intertia problem

    I'm kinda having trouble figuring out this problem...i already know that i have to use conservation of angular momentum Iiwi=Ifwf but I'm having trouble calculating the key part, the second moment of inertia. I'm pretty sure that im' supposed to be using this form of the calculation of inertia...
  47. P

    Motorcycle Intertia Dyno - Moment of Intertia for various objects?

    Hi all, Firstly - I'm not a collage student but this seemed a good place to ask the question! Any help welcome :smile: As a fun home project, I've been building a motorcycle dyno, connected to a PC via a custom made PIC based device. Have most of it worked out with regards to data...