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Moments of inertia may be expressed in units of kilogram metre squared (kg·m 2) in SI units and pound-foot-second squared (lbf·ft·s 2) in imperial or US units. The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The ...
The experiment can be performed with any object that has three different moments of inertia, for instance with a (rectangular) book, remote control, or smartphone. The effect occurs whenever the axis of rotation differs – even only slightly – from the object's second principal axis; air resistance or gravity are not necessary.
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
It is a measure of rotational inertia. [11] Moment of inertia (shown here), and therefore angular momentum, is different for each shown configuration of mass and axis of rotation. The above analogy of the translational momentum and rotational momentum can be expressed in vector form: [citation needed]
The moment of inertia of an object, symbolized by , is a measure of the object's resistance to changes to its rotation. The moment of inertia is measured in kilogram metre² (kg m 2). It depends on the object's mass: increasing the mass of an object increases the moment of inertia.
The moment of inertia is a measure of resistance to torque applied on a spinning object (i.e. the higher the moment of inertia, the slower it will accelerate when a given torque is applied). The moment of inertia can be calculated for cylindrical shapes using mass ( m {\textstyle m} ) and radius ( r {\displaystyle r} ).
An example is the calculation of the rotational kinetic energy of the Earth. As the Earth has a sidereal rotation period of 23.93 hours, it has an angular velocity of 7.29 × 10 −5 rad·s −1. [2] The Earth has a moment of inertia, I = 8.04 × 10 37 kg·m 2. [3] Therefore, it has a rotational kinetic energy of 2.14 × 10 29 J.
The linear rigid rotor model can be used in quantum mechanics to predict the rotational energy of a diatomic molecule. The rotational energy depends on the moment of inertia for the system, . In the center of mass reference frame, the moment of inertia is equal to: =