Question

A body rotates about a fixed axis with an angular acceleration of one radian/second/second, Through what angle does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s ?

Answer 1

Given in the question
Body rotates with angular accelaration, α = 1 rad/s²
Angular velocity ω = 5 rad/s
Change in angular velocity ω' = 15 rad/s
Now we have to find θ = ?

From the above condition we have

$\omega' ^{2} = \omega^{2} + 2\alpha\theta$

15² = 5²+ 2 × 1 × θ
2θ =225-25
2θ=200
θ = 100 rad .


Hope it Helps

Answer 2

It rotate during the time in which its angular velocity increases from 5 rad/s to 5 rad/s is θ = 100 rad.

Explanation:

Step 1 :

Given values in the questions,

A body rotates around a fixed axis with one radian / second angular acceleration that is,  

Body rotates with angular acceleration, α = 1 rad/s²

                                    ω = 5 rad/s

                         ω  is Angular velocity

                                ω' = 15 rad/s

                ω' is Change in angular velocity

We've got to find now θ = ?

Step 2 :

We have the above condition ,

                     $\omega^{\prime 2}=\omega^{2}+2 \alpha \theta$              

                    $15^{2}=5^{2}+2 \times 1 \times \theta$    

                    $225=25+2 \theta$

                    $225-25=2 \theta$

                     $2 \theta=200$

                    $\theta=\frac{200}{2}$    

                    $\theta=100 \mathrm{rad}$.

Thus, it rotate during the time in which its angular velocity increases from 5 rad/s to 5 rad/s is θ = 100 rad.