a spinning top is a toy designed to spin rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip due to its rotational inertia. such toys have existed since antiquity. traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion. today they are often built of plastic, and modern material
it is remarkable that this rule replaces the fairly complicated function of all three euler angles, time derivatives of euler angles, and inertia moments characterizing the rigid rotor by a simple differential operator that does not depend on time or inertia moments and differentiates to one euler angle only.
applications of dc injection braking. when power is disconnected from the motor, the rotor spins freely until friction slows it to a stop. large rotors and loads with a high moment of inertia may take a significant amount of time to stop through inherent friction alone. to reduce downtime, or possibly as an emergency safety feature, dc injection braking can be used to quickly stop the rotor.
a flywheel is a mechanical device specifically designed to efficiently store rotational energy kinetic energy . flywheels resist changes in rotational speed by their moment of inertia.the amount of energy stored in a flywheel is proportional to the square of its rotational speed and its mass. the way to change a flywheel's stored energy without changing its mass is by increasing or decreasing .
a leap second is a one-second adjustment that is occasionally applied to coordinated universal time utc , to accommodate the difference between precise time as measured by atomic clocks and imprecise observed solar time known as ut1 and which varies due to irregularities and long-term slowdown in the earth's rotation .the utc time standard, which is widely used for international .
if the mass is evenly distributed, then the center of mass of each limb is at its midpoint, and the limb has a moment of inertia of i = 1 12 ml2 about that point. it is convenient to use the angles between each limb and the vertical as the generalized coordinates defining the configuration of the system.
a synchronous electric motor is an ac motor in which, at steady state, the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of ac cycles. synchronous motors contain multiphase ac electromagnets on the stator of the motor that create a magnetic field which rotates in time with the oscillations of the line current. the rotor with permanent magnets or electromagnets turns in step with the stator field at the s
the moment of inertia of an object, symbolized by i, is a measure of the object's resistance to changes to its rotation. the moment of inertia is measured in kilogram metre² kg m² . it depends on the object's mass: increasing the mass of an object increases the moment of inertia.
rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion. the fixed axis hypothesis excludes the possibility of an axis changing its orientation, and cannot describe such phenomena as wobbling or precession.
in the case of linear forces the inertia turns out to be proportional to the mass, and in the case of rotational forces or torques, the inertia is proportional to the mass and its distribution about the axis of rotation. on the other hand maybe one word could be used for both of these concepts,.
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moment of inertia, a measure of an object's resistance to changes in its rotation rate; mi, or m i, magnitude-intensity relation, or magnitude intensity scale, used to assess the magnitude of historic earthquakes that occurred prior to the development of seismographs in the late 19th century, see mercalli intensity scale
'the scouring of the shire' is the penultimate chapter of the epic fantasy the lord of the rings by j. r. r. tolkien.the fellowship hobbits, frodo, sam, merry, and pippin, return home to the shire to find that it is under the brutal control of ruffians and their leader 'sharkey', revealed to be the wizard saruman.the ruffians have despoiled the shire, cutting down trees and destroying old .
applications of dc injection braking. when power is disconnected from the motor, the rotor spins freely until friction slows it to a stop. large rotors and loads with a high moment of inertia may take a significant amount of time to stop through inherent friction alone. to reduce downtime, or possibly as an emergency safety feature,.
a synchronous electric motor is an ac motor in which, at steady state, the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of ac cycles. synchronous motors contain multiphase ac electromagnets on the stator of the motor that create a magnetic field which rotates in time with the oscillations of the line .
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in the simplest case of circular motion at radius , with position given by the angular displacement from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: =.if is measured in radians, the arc-length from the positive x-axis around the circle to the particle is =, and the linear velocity is = = , so that =.
the easy-way is bending the workpiece along the axis with the smallest moment of inertia. for example, a piece of angle iron rolled the easy-way would be rolled along one of its flanges, while the hard-way would be along the angle itself.
the farther a given amount of material is from the neutral axis, the larger is the section modulus and hence a larger bending moment can be resisted. when designing a symmetric i-beam to resist stresses due to bending the usual starting point is the required section modulus.
by bringing part of the mass of her body closer to the axis, she decreases her body's moment of inertia. because angular momentum is the product of moment of inertia and angular velocity, if the angular momentum remains constant is conserved , then the angular velocity rotational speed of the skater must increase.