Question
A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
✓
Answer
$\omega_0=0;\ \rho=100\text{rev/s};\ \omega=2\pi;\ \rho=200\pi\text{rad/s}$$\Rightarrow\omega=\omega_0=\alpha\text{t}$
$\Rightarrow\omega=\alpha\text{t}$
$\Rightarrow\alpha=\Big(\frac{200\pi}{4}\Big)=50\pi\text{rad/s}^2$ or $25\text{rev/s}^2$
$\therefore\theta=\omega_0\text{t}+\frac{1}2{}\alpha\text{t}^2=8\times50\pi$
$=400\pi\text{rad}$
$\therefore\alpha=50\pi\text{rad/s}^2$ or $25\text{rev/s}^2$
$\theta=400\pi\text{rad}$
$\Rightarrow\omega=\alpha\text{t}$
$\Rightarrow\alpha=\Big(\frac{200\pi}{4}\Big)=50\pi\text{rad/s}^2$ or $25\text{rev/s}^2$
$\therefore\theta=\omega_0\text{t}+\frac{1}2{}\alpha\text{t}^2=8\times50\pi$
$=400\pi\text{rad}$
$\therefore\alpha=50\pi\text{rad/s}^2$ or $25\text{rev/s}^2$
$\theta=400\pi\text{rad}$
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