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  4. A wheel starts from rest and attains an angular velocity of 20 radian/s after being uniformly accelerated for 10 s. The total angle in radian through which it has turned in 10 second is

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Q. A wheel starts from rest and attains an angular velocity of $20$ radian/s after being uniformly accelerated for $10\, s$. The total angle in radian through which it has turned in $10$ second is

System of Particles and Rotational Motion

Solution:

$\omega_{f}=\omega_{l}+\alpha t$
$20=0+\alpha(10)$
$\alpha=2\, rad / s ^{2}$
Now, $\theta=\omega_{i} t+\frac{1}{2} \alpha t^{2}$
$\theta =\frac{1}{2}(2)(100)$
$=100$ radian