Flag Mechanics> Two students perform a simple experiment....
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Two students perform a simple experiment. The first student observes the orientation of a stationary disk with a single
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
mark on the edge of the rim. He then looks away. The second student then gives the disk a constant rotational acceleration of 3.0 rad/s2 for a time of 4.0 seconds; she then brings the disk to a halt with constant angular acceleration in a time of 0.10 s. The first student is now allowed to look at the disk again. (a) From the point of view of the first student, through what angle did the disk move? (b) What was the average angular velocity of the disk?

Shane Macguire , 10 Years ago
Grade upto college level
anser 1 Answers
Deepak Patra
233-804_1.PNG
The first student sees the disk rotating through a smaller number of revolutions, even smaller than 1 revolution. Therefore, he will either observe the wheel rotating through 0.91 revolutions in one direction or 1 rev – 0.91 rev = 0.09 rev in the other direction.
Last Activity: 10 Years ago
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