Moment of Inertia

Better Essays
MOMENT OF INERTIA
Chua, Richard Janssen J., PHY11L/A3 chardsenchua77@yahoo.com Abstract The moment of inertia, or also known as the rotational inertia, is the rotational analog of a rigid body to a linear or an angular motion. It is one of the fundamentals of the dynamics of rotational motion. The moment of inertia must always be in a specified chosen axis of rotation. The point of motion is basically defined as the relationship between mass and the perpendicular distance to the rotational axis.
KEYWORDS: Moment of Inertia, Rigid body, Angular motion, Axis of rotation

Introduction Moment of inertia is always defined with respect to a specific axis of rotation. The mass moment of inertia with respect to an axis is also defined as the product of the mass times the distance from the axis squared. (1) The moment of inertia of any extended object or rather a continuous mass is built up from the same basic principle. (2)
The general form of the moment of inertia involves an integration of the mass relative to the axis of rotation. (3) Density is mass per unit volume,, where the density of the body is uniform. (4)

Fig. 1: Hollow Cylinder. This image was taken from [1] (5)
Moment of Inertia of Hollow Cylinder or Ring Given the expression for the moment of inertia (4) deriving an equation of a hollow cylinder where ,

(6) Of which equation (6) can be simplified in terms of the mass in the formula of the density. Where, therefore concluding, (7)

Moment of Inertia of Disk Similar to the formula of the moment of inertia of a hollow cylinder we can use the general formula (4) to derive the moment of inertia of a disk. But instead of limits from to, the limit is set from zero to.

(8) In which and therefore concluding



References: [1] URL: http://web.phys.ntu.edu.tw/semi/ceos/general.files/Proofs%20of%20moments%20of%20inertia%20equations.htm [2] URL: http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html [3] URL: http://hyperphysics.phy-astr.gsu.edu/hbase/tdisc.html

You May Also Find These Documents Helpful

  • Satisfactory Essays

    Moment of Inertia

    • 253 Words
    • 2 Pages

    Moment of Inertia Formula The Moment of inertia is the property by the virtue of which the body resists angular acceleration. In simple words we can say it is the measure of the amount of moment given to the body to overcome its own inertia. It’s all about the body offering resistance to speed up or slow down its own motion. Moment of inertia is given by the formula Where R = Distance between the axis and rotation in m M = Mass of the object in Kg. Hence the Moment of Inertia is given in Kgm2…

    • 253 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    moment of inertia

    • 639 Words
    • 3 Pages

    Moment of Inertia Academic Resource Center What is a Moment of Inertia? • It is a measure of an object’s resistance to changes to its rotation. • Also defined as the capacity of a cross-section to resist bending. • It must be specified with respect to a chosen axis of rotation. • It is usually quantified in m4 or kgm2 Quick Note about Centroids…. • The centroid, or center of gravity, of any object is the point within that object from which the force of gravity appears to act. •…

    • 639 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    Moment of Inertia

    • 715 Words
    • 4 Pages

    ­­­Moment of Inertia 1. Abstract The goal of this study is to understand the transfer of potential energy to kinetic energy of rotation and kinetic energy of translation. The moment of inertia of the cross arm my group measured with the conservation of energy equation is: 0.01044 kg/m2 (with the mass of 15g), 0.01055 kg/m2 (with the mass of 30g), which is kind of similar to the standard magnitude of the moment of inertia of the cross arm: 0.0095 kg/m2 (Gotten by measuring the radius and the mass…

    • 715 Words
    • 4 Pages
    Satisfactory Essays
  • Good Essays

    Moment of Inertia

    • 1135 Words
    • 5 Pages

    Sadie D. Hood Lab 8: Moment of Inertia Partner: Florence Doval Due 16 November 2011 Aims: To use a centripetal force apparatus to calculate the moment of inertia of rotating weights, using theories derived from ideas of energy transfer (Im = MR2 (g/2h)(t2-t02)) and point mass appoximation (m1r12 + m2r22). Set Up Procedure First we measured the weights of two masses and wingnuts that secure them. Then we placed one of the masses on the very end of a horizontal rod on the centripetal force apparatus…

    • 1135 Words
    • 5 Pages
    Good Essays
  • Good Essays

    Mass Moment of Inertia

    • 1282 Words
    • 6 Pages

    Title: Mass Moment of Inertia Objective: To determine mass moment of inertia of a part using experimental method. Theory: If a part has been designed and built, its mass moment of inertia can be determined approximately by a simple experiment. This requires that the part be swung about any axis (other than one that passes through its CG) parallel to that about which the moment is sought and its period of pendular oscillation measured. Figure 1 shows a part of connecting rod suspended on a knife-edge…

    • 1282 Words
    • 6 Pages
    Good Essays
  • Satisfactory Essays

    Moment of inertia of a flywheel Jonathan Prevett 13/11/14 Uday Ravish Aim: To determine the moment of inertia of a flywheel. Apparatus: Fly wheel and axel, weight hanger, slotted weights, stop watch, metre ruler. Definitions: Moment of Inertia- a quantity expressing a body's tendency to resist angular acceleration Radius of Gyration- the distribution of the components of an object around an axis. Method: The weights were suspended from the axel by the cord, then we used a meter ruler to make…

    • 319 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Inertia

    • 1732 Words
    • 7 Pages

    The meaning of inertia Inertia is the property of an object which resists a change in its motion. If it is at rest it tends to remain at rest , if it is moving it tends to continue moving. Or Inertia is the reluctance of an object to move once it is at rest or the reluctance of an object to stop once it is in uniform velocity. Explanation of inertia by Newton’s First Law of Motion Newton’s First Law of Motion states that “an object will remain at rest or continue with a constant…

    • 1732 Words
    • 7 Pages
    Good Essays
  • Good Essays

    [pic] The flywheel of an engine has moment of inertia 2.5 kg•m2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8s, starting from at rest? [pic] A solid, uniform cylinder with mass 8.25kg and diameter 15cm is spinning at 200 rpm on a thin, frictionless axle that stop the cylinder axis. You design a simple friction brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic…

    • 831 Words
    • 4 Pages
    Good Essays
  • Good Essays

    Laws of Inertia

    • 1869 Words
    • 8 Pages

    Inertia (Law of Inertia) Name _____________________ Section _________ Date ______ The law of acceleration explains how a net force makes a mass accelerate. It shows how the magnitude of the acceleration depends on the magnitude of the force (directly proportional) and on the magnitude of the mass (inversely proportional). Acceleration happens only when there is an unbalanced force. Where All Forces Are Balanced No change of velocity occurs when the forces acting a body are balanced…

    • 1869 Words
    • 8 Pages
    Good Essays
  • Good Essays

    Essay on Inertia

    • 424 Words
    • 2 Pages

    person, the easier it will be to stop. We all experience this every day. The reason for this, is because of the inertia of the moving object. An object will continue to move at a constant velocity unless acted upon on an external force. The magnitude of this force is dependent on the weight of the object. It makes logical sense to think more mass will require more energy. The inertia of an object is it’s resistance to change in motion, if an object is stationary, it will stay stationary. If an object…

    • 424 Words
    • 2 Pages
    Good Essays