A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

Ques: A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

Solution: In the given question, some known values are given as mentioned below: 

• Initial angular velocity of the fan, ω_i = 5 rad/s (Given)
• Final angular velocity of the fan, ω_f = 15 rad/s​ (Given)
• Angular acceleration, α = 1 rad/sec² ​(Given)

Here we will apply the equation of rotational motion for constant angular acceleration which is given as: 

ω_f² = ω_i² + 2αθ

⇒ θ = \(\frac{\omega_f^2 - \omega_i^2}{2 \alpha}\)

Where 

• ω_f = final angular velocity
• ω_i = initial angular velocity
• α = angular acceleration
• θ = angular displacement of the body during the time in which its angular velocity

Using the equation of rotational motion, angular displacement of the fan, is given by 

θ = \(\frac{15^2-5^2}{2 \times 1}\) = \(\frac{225-25}{2}\) = 100 rad

Hence, the body rotates with an angular displacement of 100 rad during the time in which its angular velocity increases from 5 rad/s to 15 rad/s.

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