Problem 1
The figure shows the plot of angular displacement and time of a rotating disc. The magnitude of angular velocity is minimum for motion in :
(a) segment OA (b) segment AB (c) segment BC (d) segment CD
Answer
The magnitude of slope of line CD is zero. The magnitude of slope of line AC is finite and is greater than that of line OA.
Hence, option (d) is correct.
Problem 2
The figure shows the plot of angular displacement and time of a rotating disc. Corresponding to the segments marked on the plot, the direction of rotation is as :
(a) disk rotates in clockwise direction in the segments OA and AB.
(b) disk rotates in clockwise direction in the segment OA, but in anti-clockwise direction in the segment AB
(c) disk rotates in anti-clockwise direction in the segment AC.
(d) disk rotates in anti-clockwise direction in the segment CD.
Answer
The direction of rotation is determined by the sign of angular velocity. In turn, the sign of angular velocity is determined by the sign of the slope on angular displacement ? time plot. The sign of slope is negative for line OA, positive for line AC and zero for line CD. The negative angular velocity indicates anti-clockwise rotation and positive angular velocity indicates clockwise rotation.
Hence, options (b) and (c) are correct.
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