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5.10. Kinetic energy of a rotating body

Lecture



The kinetic energy of a body moving in an arbitrary way is equal to the sum of the kinetic energies of all n material points on which this body can be broken:

  5.10.  Kinetic energy of a rotating body

If the body rotates around a fixed axis with an angular velocity   5.10.  Kinetic energy of a rotating body , then the linear velocity of the i-th point is   5.10.  Kinetic energy of a rotating body where   5.10.  Kinetic energy of a rotating body , is the distance from this point to the axis of rotation. Consequently.

  5.10.  Kinetic energy of a rotating body (5.11)

Where   5.10.  Kinetic energy of a rotating body - moment of inertia of the body relative to the axis of rotation.

In the general case, the motion of a rigid body can be represented as the sum of two motions — a translational with a velocity equal to the velocity   5.10.  Kinetic energy of a rotating body center of inertia of the body, and rotation with angular velocity   5.10.  Kinetic energy of a rotating body   around the instantaneous axis passing through the center of inertia. The expression for the kinetic energy of the body is converted to

  5.10.  Kinetic energy of a rotating body (5.12)

Where   5.10.  Kinetic energy of a rotating body - moment of inertia of the body relative to the instantaneous axis of rotation passing through the center of inertia.


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Physical foundations of mechanics

Terms: Physical foundations of mechanics