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?

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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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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?

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4.A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:

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6.Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

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