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प्रश्न
A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
उत्तर
Given
t = 4s
Initial angular velocity = \[\omega_0 = 0\]
Final angular velocity = \[\omega = 100 \text{ rev/s}\]
\[\omega = \omega_0 + \alpha t\]
\[\alpha = \frac{\omega}{t}\]
\[\alpha = \frac{100}{4}\text{ rev/ s}^2 = 25\text{ rev/ s}^2 \]
Now, we have
\[\theta = \omega_0 t + \frac{1}{2}\alpha t^2 \]
\[ \Rightarrow \theta = \frac{1}{2} \times 25 \times 16\]
\[ = 200^\circ\]
\[ \Rightarrow \theta = 200 \times 2\pi\text{ radians}\]
\[ = 400\pi\text{ radians}\]
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