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Lecture# Gyroscopes: Conservation of Angular Momentum

Description

This lecture starts with the instructor encouraging feedback on course evaluations. The concept of gyroscopes is introduced, explaining their role in maintaining stability through conservation of angular momentum. The lecture covers the dynamics of rotating objects, moments of inertia calculations, and gyroscopic effects. Demonstrations with rotating wheels illustrate the principles of angular momentum conservation. The instructor showcases how gyroscopes resist changes in orientation due to their rotational motion, emphasizing the importance of understanding the physics behind gyroscopic behavior.

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In course

Instructors (2)

PHYS-101(f): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr

Related concepts (124)

Rotation around a fixed axis

Rotation around a fixed axis or axial rotation is a special case of rotational motion around a axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

Axis–angle representation

In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction (geometry) of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the rotation about the axis. Only two numbers, not three, are needed to define the direction of a unit vector e rooted at the origin because the magnitude of e is constrained.

Euler's rotation theorem

In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group. The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry.

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.

Rotating spheres

Isaac Newton's rotating spheres argument attempts to demonstrate that true rotational motion can be defined by observing the tension in the string joining two identical spheres. The basis of the argument is that all observers make two observations: the tension in the string joining the bodies (which is the same for all observers) and the rate of rotation of the spheres (which is different for observers with differing rates of rotation). Only for the truly non-rotating observer will the tension in the string be explained using only the observed rate of rotation.

Related lectures (752)

Rigid Body with Fixed Axis and GyroscopesPHYS-101(f): General physics : mechanics

Explores gyroscopes, gyroscopic effects, and the dynamics of spinning objects with fixed axes.

Angular Momentum TheoremPHYS-101(g): General physics : mechanics

Covers torque force, angular momentum theorem, gyroscopic effects, and procession of the earth's axis.

Rigid Body Dynamics and GyroscopesPHYS-101(f): General physics : mechanics

Explores moments of inertia, energy of rigid bodies, gyroscopes, and unbalanced wheels.

Angular Momentum Theorem: Gyroscope DynamicsPHYS-101(g): General physics : mechanics

Explores the angular momentum theorem in gyroscope dynamics and symmetrical motion.

Rotational Dynamics: Moment of Inertia and ForcesPHYS-101(c): General physics : mechanics (IN I)

Covers rotational dynamics, focusing on moment of inertia and forces involved in rotational motion.