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Rotational Inertia
Rotational inertia is the tendency of a rotating object to remain rotating unless a torque is applied to it.
Learning Objectives

Apply rotational inertia to describe behavior of a rotating object

Explain the relationship between the force, mass, radius, and angular acceleration
Key Points

The farther the force is applied from the pivot, the greater the angular acceleration.

Angular acceleration is inversely proportional to mass.

The equation τ = m(r^2)α is the rotational analog of Newton's second law (F=ma), where torque is analogous to force, angular acceleration is analogous to translational acceleration, and mr2 is analogous to mass (or inertia).
Terms

torque
A rotational or twisting effect of a force; (SI unit newtonmeter or Nm; imperial unit footpound or ftlb)

rotational inertia
The tendency of a rotating object to remain rotating unless a torque is applied to it.
Full Text
If you have ever spun a bike wheel or pushed a merrygoround, you have experienced the force needed to change angular velocity. Our intuition is reliable in predicting many of the factors that are involved. For example, we know that a door opens slowly if we push too close to its hinges. Furthermore, we know that the more massive the door, the more slowly it opens. The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration; another implication is that angular acceleration is inversely proportional to mass. These relationships should seem very similar to the familiar relationships among force, mass, and acceleration embodied in Newton's second law of motion. There are, in fact, precise rotational analogs to both force and mass.
Rotational inertia, as illustrated in , is the resistance of objects to changes in their rotation. In other words, a rotating object will stay rotating and a nonrotating object will stay nonrotating unless acted on by a torque. This should remind you of Newton's First Law.
To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force F on a point mass m that is at a distance r from a pivot point.
Because the force is perpendicular to r, an acceleration
Recall that torque is the turning effectiveness of a force. In this case, because F is perpendicular to r, torque is simply τ=Fr. So, if we multiply both sides of the equation above by r, we get torque on the lefthand side. That is, rF = mr^{2}α, or
τ = mr^{2}α.
This equation is the rotational analog of Newton's second law (F=ma), where torque is analogous to force, angular acceleration is analogous to translational acceleration, and mr^{2} is analogous to mass (or inertia). The quantity mr^{2} is called the rotational inertia or moment of inertia of a point mass m a distance r from the center of rotation.
Different shapes of objects have different rotational inertia which depend on the distribution of their mass.
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Key Term Reference
 Law
 Appears in this related concepts: Physics and Other Fields, Damped Harmonic Motion, and Models, Theories, and Laws
 acceleration
 Appears in this related concepts: Motion with Constant Acceleration, Graphical Interpretation, and Applications and ProblemSolving
 angular
 Appears in this related concepts: Wavelength, Freqency in Relation to Speed, Bohr Orbits, and Constant Angular Acceleration
 angular acceleration
 Appears in this related concepts: Relationship Between Torque and Angular Acceleration, Angular Acceleration, Alpha, and Conservation of Angular Momentum
 angular velocity
 Appears in this related concepts: Angular vs. Linear Quantities, Angular Velocity, Omega, and Kepler's Second Law
 equation
 Appears in this related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 force
 Appears in this related concepts: Newton and His Laws, Work Done by a Variable Force, and Driven Oscillations and Resonance
 inertia
 Appears in this related concepts: Rotational Kinetic Energy: Work, Energy, and Power, The Impact of Culture on an Organization, and The First Law: Inertia
 mass
 Appears in this related concepts: Physical and Chemical Properties of Matter, Mass Spectrometer, and Mass
 moment of inertia
 Appears in this related concepts: Applications of Multiple Integrals, Internal Energy of an Ideal Gas, and ProblemSolving Techniques
 motion
 Appears in this related concepts: Motion Diagrams, TwoComponent Forces, and Moving Source
 perpendicular
 Appears in this related concepts: The Cross Product, Circular Motion, and Normal Forces
 point mass
 Appears in this related concepts: Moment of Inertia, Weight of the Earth, and Introduction to Simple Harmonic Motion
 resistance
 Appears in this related concepts: Resistors in Parallel, Resisitors in Series, and Ecology of Ecosystems
 rotation
 Appears in this related concepts: Rotational Collisions, Lever Systems, and Center of Mass and Translational Motion
 velocity
 Appears in this related concepts: Rolling Without Slipping, Arc Length and Speed, and Tangent and Velocity Problems
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Cite This Source
Source: Boundless. “Rotational Inertia.” Boundless Physics. Boundless, 14 Jan. 2015. Retrieved 24 Mar. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/rotationalkinematicsangularmomentumandenergy9/dynamics84/rotationalinertia3256299/