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  2. List of moments of inertia - Wikipedia

    en.wikipedia.org/wiki/List_of_moments_of_inertia

    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.

  3. Moment of inertia - Wikipedia

    en.wikipedia.org/wiki/Moment_of_inertia

    There is an interesting difference in the way moment of inertia appears in planar and spatial movement. Planar movement has a single scalar that defines the moment of inertia, while for spatial movement the same calculations yield a 3 × 3 matrix of moments of inertia, called the inertia matrix or inertia tensor. [6] [7]

  4. Inertia - Wikipedia

    en.wikipedia.org/wiki/Inertia

    Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics , and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [ 1 ]

  5. Euler's equations (rigid body dynamics) - Wikipedia

    en.wikipedia.org/wiki/Euler's_equations_(rigid...

    One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant. Using a reference frame such as that at the center of mass, the frame's position drops out of the equations. In any rotating reference frame, the time derivative must be replaced so that the equation becomes

  6. Newton–Euler equations - Wikipedia

    en.wikipedia.org/wiki/Newton–Euler_equations

    With respect to a coordinate frame whose origin coincides with the body's center of mass for τ() and an inertial frame of reference for F(), they can be expressed in matrix form as:

  7. Rigid body - Wikipedia

    en.wikipedia.org/wiki/Rigid_body

    When the angular velocity is expressed with respect to a coordinate system coinciding with the principal axes of the body, each component of the angular momentum is a product of a moment of inertia (a principal value of the inertia tensor) times the corresponding component of the angular velocity; the torque is the inertia tensor times the ...

  8. Rigid rotor - Wikipedia

    en.wikipedia.org/wiki/Rigid_rotor

    A rigid body can be (partially) characterized by the three eigenvalues of its moment of inertia tensor, which are real nonnegative values known as principal moments of inertia. In microwave spectroscopy—the spectroscopy based on rotational transitions—one usually classifies molecules (seen as rigid rotors) as follows: spherical rotors

  9. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    If one also diagonalizes the rigid body's moment of inertia tensor (with nine components, six of which are independent), then one has a set of coordinates (called the principal axes) in which the moment of inertia tensor has only three components. The angular velocity of a rigid body takes a simple form using Euler angles in the moving frame.