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A rotating object has a moment of inertia of 1.2 kg m² and an initial angular velocity of 0 rad/sec. If its angular acceleration is 25 rad/sec² and the rotational kinetic energy reaches 1500 J, how much time does it take?

1. t = 2 seconds
2. t = 3 seconds
3. t = 4 seconds
4. t = 5 seconds

Correct answer: t = 3 seconds

Solution

The rotational kinetic energy is given by Eₑ = (1/2)Iω². Solving for ω, we get ω = √(2Eₑ/I). Substituting Eₑ = 1500 J and I = 1.2 kg m², ω = √(2*1500/1.2) = 50 rad/s. Using ω = ω₁ + αt, and given ω₁ = 0, α = 25 rad/s², and ω = 50 rad/s, t = ω/α = 50/25 = 2 s.

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