Question

A wheel is rotating with angular velocity 2 rad/s. It is subjected to uniform angular acceleration 2.0 rad/
(a) How much angular velocity does the wheel acquire after 10 s?
(b) How many complete revolution it makes in this time interval?​

Answer 1

Given:

A wheel is rotating with angular velocity 2 rad/s. It is subjected to uniform angular acceleration 2.0 rad/s.

To find:

• How much angular velocity does the wheel acquire after 10s ?

• How many complete revolution it makes in this time interval?

Calculation:

Let initial angular velocity be $\omega1$ and final angular velocity be $\omega2$.

Applying Equations of Rotational Kinematics:

$\therefore \: \omega2 = \omega1 + \alpha t$

$= > \: \omega2 =2+ (2 \times 10)$

$= > \: \omega2 =2+ 20$

$\boxed{ = > \: \omega2 =22 \: rad \: {s}^{ - 1} }$

Now , applying the 3rd Equation of Kinematics:

$\therefore \: \theta = (\omega1 )t + \dfrac{1}{2} \alpha {t}^{2}$

$= > \: \theta = (2 \times 10) + \dfrac{1}{2} (2) {(10)}^{2}$

$= > \: \theta = 22+ 100$

$= > \: \theta = 122 \: rad$

We need to convert the unit of angular displacement:

$= > \theta = \dfrac{122}{2\pi}$

$= > \theta = \dfrac{61}{\pi}$

$\boxed{= > \theta = 19.41 \: revolutions}$

HOPE IT HELPS.