Moment of Inertia
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
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