Find the angular velocity of a body rotating with an acceleration of 2 rev - s 2 as it completes the 5 th revolution after the start-

Angular displacement of the body, #952;=5 #160;rev=10 #960; #160;rad #945;=2 #160;rev/s2=4 #960; #160;rad/s2Initial #160;angular #160;veloc ...

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Standard IX

Geography

Rotation of Earth and Its Effects

Find the angu...

Question

Find the angular velocity of a body rotating with an acceleration of 2 rev/s² as it completes the 5th revolution after the start.

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Solution

Angular displacement of the body,
$θ = 5 rev = 10 π rad α = 2 rev / s^{2} = 4 π rad / s^{2} Initial angular velocity, ω_{0} = 0 Final angular velocity, ω = ? ω^{2} = (2 αθ) \Rightarrow ω = \sqrt{2 \times 4 π \times 10 π} = 4 π \sqrt{5} rad / s \Rightarrow ω = 2 \sqrt{5} rev / s$

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Q. Find the angular velocity of a body rotating with an acceleration of 2rev/s² as it completes the 5th revolution after the start.[Concepts of Physics]
BOOK ANSWER - 4.47 rev/s
MY SOLUTION
In one revolution the distance covered is 2π,
so, in 5 revolution the distance moved is 10π
Angular Acceleration = 2rev/s
Initial angular velocity = 0
Final angular velocity = ?
So using equation,
v²= u²+ 2as
= 0 + 2* 2*10π
= 40π
v = 11.2rev/sec
Why my Answer is different? Where and what I am missing.
NOTE : I can't write omega on my tablet also you understand it well that we can type only that which is given in keyboard.

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Find the angular velocity of a body rotating with an acceleration of 2 rev/s2 as it completes the 5th revolution after the start.

Angular displacement of the body, θ=5 rev=10π radα=2 rev/s2=4π rad/s2Initial angular velocity, ω0=0Final angular velocity, ω=?ω2=2αθ⇒ω=2×4π×10π =4π5 rad/s ⇒ω=25 rev/s

Find the angular velocity of a body rotating with an acceleration of 2 rev/s² as it completes the 5th revolution after the start.

Angular displacement of the body,
$θ = 5 rev = 10 π rad α = 2 rev / s^{2} = 4 π rad / s^{2} Initial angular velocity, ω_{0} = 0 Final angular velocity, ω = ? ω^{2} = (2 αθ) \Rightarrow ω = \sqrt{2 \times 4 π \times 10 π} = 4 π \sqrt{5} rad / s \Rightarrow ω = 2 \sqrt{5} rev / s$