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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. - Physics

Sum

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.

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Solution

Given

= 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

\[\theta = \omega_0 t + \frac{1}{2}\alpha t^2 \]

\[ \Rightarrow \theta = \frac{1}{2} \times 25 \times 16\]

\[ = 200^\circ\]

\[ \Rightarrow \theta = 200 \times 2\pi\text{ radians}\]

\[ = 400\pi\text{ radians}\]

Concept: Equations of Rotational Motion
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 10 Rotational Mechanics
Q 1 | Page 195
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