Question

A wheel has an angular acceleration of $3rad/{s^2}$ and an initial angular speed of $2rad/s$. In a time of $2\sec $, it has rotated through an angle (in radian) of
A) $10rad$
B) $20rad$
C) $15rad$
D) $25rad$

Answer 1

Hint: First of all we have to separate the given quantities and convert them into S.I units if they aren’t. now after that we have to define the equation of the angular motion for the angular displacement so that we can use it , $\theta = {\omega _o}t + \dfrac{1}{2}\alpha {t^2}$ . Here we can see that we have all the quantir=ties required for the equation, so in the next step, we just have to put it and get the answer.

Complete step by step answer:
Given,
Initial angular speed of the wheel is ${\omega _o} = 2rad/s$
Angular acceleration of the wheel is $\alpha = 3rad/{s^2}$
Time in which we have to calculate the rotation of the wheel is $t = 2s$

Step 1: We have to efine an equation for the angular displacement so that we can equate the given values. The equation is
$\theta = {\omega _o}t + \dfrac{1}{2}\alpha {t^2}$
Step 2: Now we have to put the given values in the equation in order to get the given answer
$
\Rightarrow \theta = {\omega _o}t + \dfrac{1}{2}\alpha {t^2} \\
\Rightarrow \theta = 2 \times 2 + \dfrac{1}{2} \times 3 \times {2^2} \\
\Rightarrow \theta = 4 + 6 = 10rad \\
 $

Therefore the required angle is $10rad$. Hence, option (A) is correct..

Note:
The angular displacement of a body is the angle in radians (degrees, revolutions) through which a point revolves around a centre or line has been rotated in a specified sense about a specified axis. Therefore we can say that it will vary even in the same plane if we alter the axis of rotation.