Angular speed, ω is the rate at which an object rotates. Although usually measured in radians per second, ω can also be expressed in degrees per second. For instance, consider a merry-go-round. Figure shows its angular speed as a function of time, t. In this graph, a positive value of ω indicates counterclockwise rotation.
A "complete revolution" occurs when the merry-go-round turns through one full circle.
(i) Between t = 0 s and t = 10 s, about how many revolutions does the merry-go-round complete?
Text Solution
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Ans.
(i)
Sol. Angle = Area under ω – t graph = 700º
∴ n = 
= 1.94 ≈ 2
(ii)
Sol. ω is positive and decreasing. Hence, merry-go-round is rotating counter clockwise and it is slowing down.
(iii)
Sol. Between t = 30 to t = 40, ω is negative and its magnitude is decreasing. Hence, merry-go-round is rotating clockwise and it is slowing down.
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