inertia

(noun)

The property of a body that resists any change to its uniform motion; equivalent to its mass.

Related Terms

  • uniform motion
  • angular velocity
  • friction
  • torque
  • acceleration

(noun)

the tendency of an object to resist any change in its motion

Related Terms

  • uniform motion
  • angular velocity
  • friction
  • torque
  • acceleration

Examples of inertia in the following topics:

  • Moment of Inertia

    • Newton's first law, which describes the inertia of a body in linear motion, can be extended to the inertia of a body rotating about an axis using the moment of inertia.
    • Moment of inertia also depends on the axis about which you rotate an object.
    • The basic relationship between the moment of inertia and the angular acceleration is that the larger the moment of inertia, the smaller the angular acceleration.
    • A brief introduction to moment of inertia (rotational inertia) for calculus-based physics students.
    • Identify a property of a mass described by the moment of inertia
  • Rotational Inertia

    • Rotational inertia is the tendency of a rotating object to remain rotating unless a torque is applied to it.
    • Rotational inertia, as illustrated in , is the resistance of objects to changes in their rotation.
    • 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 mr2 is analogous to mass (or inertia).
    • The quantity mr2 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.
  • The Physical Pendulum

    • The period of a physical pendulum depends upon its moment of inertia about its pivot point and the distance from its center of mass.
    • In this case, the pendulum's period depends on its moment of inertia around the pivot point .
    • where α is the angular acceleration, τ is the torque, and I is the moment of inertia.
    • The moment of inertia of the rigid rod about its center is:
    • A change in shape, size, or mass distribution will change the moment of inertia.
  • Rotational Kinetic Energy: Work, Energy, and Power

    • Looking at rotational energy separately around an object's axis of rotation yields the following dependence on the object's moment of inertia:
    • where $\omega$ is the angular velocity and $I$ is the moment of inertia around the axis of rotation.
    • In the rotating system, the moment of inertia takes the role of the mass and the angular velocity takes the role of the linear velocity.
    • The Earth has a moment of inertia, I = 8.04×1037 kg·m2.
    • The ratio depends on the moment of inertia of the object that's rolling.
  • Relationship Between Torque and Angular Acceleration

    • Torque is equal to the moment of inertia times the angular acceleration.
    • Torque and angular acceleration are related by the following formula where is the objects moment of inertia and $\alpha$ is the angular acceleration .
    • If you replace torque with force and rotational inertia with mass and angular acceleration with linear acceleration, you get Newton's Second Law back out.
    • The net torque about an axis of rotation is equal to the product of the rotational inertia about that axis and the angular acceleration, as shown in Figure 1 .
  • The First Law: Inertia

    • Newton’s first law of motion describes inertia.
    • Sometimes this first law of motion is referred to as the law of inertia.
    • Inertia is the property of a body to remain at rest or to remain in motion with constant velocity.
    • Some objects have more inertia than others because the inertia of an object is equivalent to its mass.
  • Conservation of Angular Momentum

    • When she does this, the rotational inertia decreases and the rotation rate increases in order to keep the angular momentum $L = I \omega$ constant.
    • (I: rotational inertia, $\omega$: angular velocity)
    • In the next image, her rate of spin increases greatly when she pulls in her arms, decreasing her moment of inertia.
  • Relationship Between Linear and Rotational Quantitues

    • The description of motion could be sometimes easier with angular quantities such as angular velocity, rotational inertia, torque, etc.
  • Conservation of Energy in Rotational Motion

    • Kinetic energy (K.E.) in rotational motion is related to moment of rotational inertia (I) and angular velocity (ω):
  • Rotational Collisions

    • As we would expect, an object that has a large moment of inertia I, such as Earth, has a very large angular momentum.
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