![]() ![]() Where moment of inertia appears in physical quantities The general form of the moment of inertia involves an integral. The moment of inertia of any extended object is built up from that basic definition. The moment of inertia of a point mass with respect to an axis is defined as the product of the mass times the distance from the axis squared. Moment of inertia is defined with respect to a specific rotation axis. ![]() That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses. For a point mass, the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr 2. The moment of inertia must be specified with respect to a chosen axis of rotation. It appears in the relationships for the dynamics of rotational motion. Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. This is called precession, and is analogous to the orbit of a mass under a central force. This changes its direction but not its magnitude, causing the tip of the axle to trace out a circle. If a spinning wheel and axle is supported by one end of the axle, then the torque produced by the weight of the wheel and axle produces a torque that is perpendicular to the angular momentum of the wheel. Acting perpendicular to the velocity, it provides the necessary centripetal force to keep it in a circle. With the appropriate balance of force, a circular orbit can be produced by a force acting toward the center. This is because the product of moment of inertia and angular velocity must remain constant, and halving the radius reduces the moment of inertia by a factor of four. If the string is pulled down so that the radius is half the original radius, then conservation of angular momentum dictates that the ball must have four times the angular velocity. Using a string through a tube, a mass is moved in a horizontal circle with angular velocity ω. ![]() HyperPhysics***** Mechanics ***** RotationĬonservation of linear momentum dictates that when a mass strikes an equal mass at rest and sticks to it, the combination must move at half the velocity, because the product of mass and velocity must remain constant. The motion here is enabled due to the gravitational attraction between the Sun and planets.Moment of Inertia Rotational-Linear Parallels More comparisons between linear and angular motion In this figure, the planets are revolving around the sun in their actual defined axes and are under the effect of rotational motion. This force is responsible for the act of rotation and if the force isĭue to gravity, then it is only seen in celestial bodies. Whenever an object rotates, it creates a force that enables it to do so. Not every rotational motion depends on gravity. Gravity, however, also affects rotational motion, whenever any celestial body, for instance, revolves around any other body or whenever the Earth revolves around the Sun, the force which causes the motion is only because of the gravitational attraction between them. And depending on the radius of the rotational motion, the tangential velocity of an object is considered. Depending on the change in angle of an object, we consider angular velocity. Much like translational motion, rotational motion is also dependent on position or angle of an object, the curved path it may follow, its velocity, and acceleration, the time period, etc. ![]()
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