Serway_PSE_quick_ch10.ppt

Serway_PSE_quick_ch10.ppt - Physics for Scientists and...

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Physics for Scientists and Engineers, 6e Chapter 10 – Rotation of a Rigid Object about a Fixed Axis
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A rigid object is rotating in a counterclockwise sense around a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid object. Which of the sets can only occur if the rigid object rotates through more than 180°? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1. 3 rad, 6 rad 2. -1 rad, 1 rad 3. 1 rad, 5 rad
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For a rotation of more than 180 ° , the angular displacement must be larger than π = 3.14 rad. The angular displacements in the three choices are (1) 6 rad – 3 rad = 3 rad; (2) 1 rad – (-1) rad = 2 rad; (3) 5 rad – 1 rad = 4 rad.
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Suppose that the change in angular position for each of the pairs of values in question 1 occurs in 1 s. Which choice represents the lowest average angular speed? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1. 3 rad, 6 rad 2. -1 rad, 1 rad 3. 1 rad, 5 rad
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Because all angular displacements occur in the same time interval, the displacement with the lowest value will be associated with the lowest average angular speed.
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A rigid object is rotating with an angular speed ω < 0. The angular velocity vector ω and the angular acceleration vector α are antiparallel. The angular speed of the rigid object is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1. clockwise and increasing 2. clockwise and decreasing 3. counterclockwise and increasing 4. counterclockwise and decreasing
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The fact that ω is negative indicates that we are dealing with an object that is rotating in the clockwise direction. We also know that when ω and α are antiparallel, ω must be decreasing – the object is slowing down. Therefore, the object is spinning more and more slowly (with less and less angular speed) in the clockwise, or negative, direction.
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Consider again the pairs of angular positions for the rigid object. If the object starts from rest at the initial angular position, moves counterclockwise with constant angular
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