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Lecture# Rotation Dynamics: Symmetry and Gyroscopic Effects

Description

This lecture covers the dynamics of rotation around an axis of symmetry, gyroscopic effects, and rotation around a fixed instantaneous axis. It explores the behavior of non-rigid objects, such as containers filled with granules, and the critical angles for rolling down inclined planes. Theoretical approaches and experimental studies are discussed, emphasizing the interplay between mass distribution and moment of inertia. The lecture also delves into the oscillation frequency of systems and energy dissipation in varying conditions.

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Related concepts (108)

Rigid body dynamics

In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior.

Moment of inertia

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

Rigid rotor

In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles. A special rigid rotor is the linear rotor requiring only two angles to describe, for example of a diatomic molecule. More general molecules are 3-dimensional, such as water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor).

Conservatism

Conservatism is a cultural, social, and political philosophy that seeks to promote and to preserve traditional institutions, practices, and values. The central tenets of conservatism may vary in relation to the culture and civilization in which it appears. In Western culture, depending on the particular nation, conservatives seek to promote a range of social institutions such as the nuclear family, organized religion, the military, property rights, and monarchy.

Inertia

Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law of motion. After some other definitions, Newton states in his first law of motion: LAW I. Every object perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

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