the angular velocity of a rotating body increase uniformly from 100rad/sec to 200rad/sec in 20sec,how many revolutions will the body execute during this time
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the angular velocity of a rotating body increase uniformly from 100rad/sec to 200rad/sec in 20sec,how many revolutions will the body execute during this time
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Verified answer
Given :
The angular velocity of a rotating body increase uniformly from 100rad/s to 200rad/s in 20s.
To Find :
No. of revolutions completed by the body.
Solution :
❖ First of all we need to find angular acceleration of the body.
Formula : α = (ω' - ω) / t
» α denotes angular acceleration
» ω' denotes final angular velocity
» ω denotes initial angular velocity
» t denotes time
By substituting the given values;
➙ α = (200 - 100) / 20
➙ α = 100/20
➙ α = 5 rad/s²
Now let's calculate angular distance covered by the body
➠ ω'² - ω² = 2αθ
➠ (200)² - (100)² = 2(5)θ
➠ 40000 - 10000 = 10 θ
➠ 30000 = 10 θ
➠ θ = 3000 rad
No. of revolutions :
➝ n = θ / 2π
➝ n = 3000/2(3.14)
➝ n ≈ 477 revolutions