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2.5. The relationship of angular and linear quantities

Lecture



Separate points of a rotating body have different linear velocities. 2.5.  The relationship of angular and linear quantities . The speed of each point, being tangential to the corresponding circle, continuously changes its direction. Speed ​​magnitude 2.5.  The relationship of angular and linear quantities determined by the speed of body rotation 2.5.  The relationship of angular and linear quantities and the distance R of the considered point from the axis of rotation. Let for a small period of time 2.5.  The relationship of angular and linear quantities the body turned to the corner 2.5.  The relationship of angular and linear quantities (figure 2.4). A point located at a distance R from the axis passes the path equal to

2.5.  The relationship of angular and linear quantities

Linear velocity of a point by definition.

2.5.  The relationship of angular and linear quantities (2.6)

Find the linear acceleration points of the rotating body. Normal acceleration:

2.5.  The relationship of angular and linear quantities

substituting the value of speed from (2.6), we find:

2.5.  The relationship of angular and linear quantities (2.7)

Tangential acceleration

2.5.  The relationship of angular and linear quantities

2.5.  The relationship of angular and linear quantities

Using the same relation (2.6) we get

2.5.  The relationship of angular and linear quantities (2.8)

Thus, both normal and tangential accelerations grow linearly with the distance of the point from the axis of rotation.

created: 2014-09-13
updated: 2022-01-11
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Physical foundations of mechanics

Terms: Physical foundations of mechanics