Question
A wheel starting from rest is uniformly accelerated at $4 ~rad/-s^2$ for 10 seconds.It is allowed to rotate uniformly for the next 10 seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.
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Answer
Area under the curve will decide the total angle rotated$\therefore$ Maximum angular velocity = 4 × 10 = 40 rad/-s
Therefore, area under the curve $=\frac{1}2{}\times10\times40+40\times10+\frac{1}{2}\times40\times10$$=800\text{rad}$
$\therefore$ Total angle rotated = 800rad.
Therefore, area under the curve $=\frac{1}2{}\times10\times40+40\times10+\frac{1}{2}\times40\times10$$=800\text{rad}$
$\therefore$ Total angle rotated = 800rad.
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