The angular speed of the rotating rigid body is increased from 4ω to 5ω. The percentage increase in its K.E. is :
Correct answer: D. 56%
- A. 20%
- B. 25%
- C. 125%
- D. 56%
Explanation
K.E. = ½ I ω² ⇒ K.E. ∝ ω²K.E.i ∝(4)²= 16ω²K.E.f ∝(5)²= 25ω²% increase in K.E. = (KEf − KEᵢ) / KEᵢ × 100= (25 − 16) / 16 × 100= 9/16 × 100= 56.25%The percentage increase is 56.25%. Among the given options, 56% is the closest and most appropriate answer.
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About Angular Velocity
Angular velocity describes how quickly angular displacement changes with time, with ω = Δθ/Δt and units of radians per second. Questions relate angular and linear motion through v = rω, use the direction given by the right hand rule, and distinguish angular velocity from angular acceleration and ordinary frequency.
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