A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point’s angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible.QuestionHow can the graph be used to determine the angular speed of the disk after 2s? Justify your selection.ResponsesDetermine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the final angular velocity of the point on disk.Determine the area bound by the line and the horizontal axis from 0 seconds to 2 seconds , because this area represents the final angular velocity of the point on disk.Determine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the change in the angular velocity of the point on disk.Determine the area bound by the line and the horizontal axis from 0 seconds to 2 seconds , because this area represents the change in the angular velocity of the point on disk.Determine the vertical-axis intercept, because this value represents the final angular velocity of the point on disk.Determine the vertical-axis intercept, because this value represents the final angular velocity of the point on disk.Determine the slope of the line, because this value represents the change in the angular velocity of the point on disk.
Question
A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point’s angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible.QuestionHow can the graph be used to determine the angular speed of the disk after 2s? Justify your selection.ResponsesDetermine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the final angular velocity of the point on disk.Determine the area bound by the line and the horizontal axis from 0 seconds to 2 seconds , because this area represents the final angular velocity of the point on disk.Determine the area bound by the line and the horizontal axis from 0s to 2s , because this area represents the change in the angular velocity of the point on disk.Determine the area bound by the line and the horizontal axis from 0 seconds to 2 seconds , because this area represents the change in the angular velocity of the point on disk.Determine the vertical-axis intercept, because this value represents the final angular velocity of the point on disk.Determine the vertical-axis intercept, because this value represents the final angular velocity of the point on disk.Determine the slope of the line, because this value represents the change in the angular velocity of the point on disk.
Solution
The correct response would be: "Determine the area bound by the line and the horizontal axis from 0s to 2s, because this area represents the change in the angular velocity of the point on disk."
This is because the area under an acceleration-time graph gives the change in velocity. In this case, since we're dealing with angular quantities, the area under the angular acceleration-time graph gives the change in angular velocity.
To find the final angular velocity, you would then add this change in angular velocity to the initial angular velocity. Since the initial angular velocity is given as 3 rad/s clockwise (which is the negative direction), you would subtract the change in angular velocity from 3 rad/s.
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