# A wheel rotating with a uniform acceleration covers 100 revolution in the first 10 seconds after the start. What is the angular velocity at the end of 10 seconds?

May 2, 2018

The angular velocity is $= 125.7 r a {\mathrm{ds}}^{-} 1$

#### Explanation:

The angle covered is $\theta = n \cdot 2 \pi = 100 \times 2 \pi = 200 \pi r a d$

The time is $t = 10 s$

The initial angular velocity is ${\omega}_{0} = 0 r a {\mathrm{ds}}^{-} 1$

Let the angular acceleration be $= \alpha r a {\mathrm{ds}}^{-} 2$

Apply the equation

$\theta = {\omega}_{0} t + \frac{1}{2} \alpha {t}^{2}$

$200 \pi = \frac{1}{2} \alpha \times 100$

$\alpha = 4 \pi r a {\mathrm{ds}}^{-} 2$

Apply the equation

$\omega \left(t\right) = {\omega}_{0} + \alpha t$

$\omega \left(10\right) = 0 + 4 \pi \times 10 = 40 \pi r a {\mathrm{ds}}^{-} 1$

The angular velocity is $= 125.7 r a {\mathrm{ds}}^{-} 1$