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.

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