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A rotating body has I = 2 kgm², ω₀ = 2π rad/sec, and t = 1 min. The angular acceleration α and torque τ are given by:

1. α = -π / 30 rad/sec², τ = -π / 15 N·m
2. α = -π / 30 rad/sec², τ = -π / 30 N·m
3. α = -π / 60 rad/sec², τ = -π / 15 N·m
4. α = -π / 30 rad/sec², τ = -π / 15 N·m

Correct answer: α = -π / 30 rad/sec², τ = -π / 15 N·m

Solution

The angular acceleration is calculated using α = (ω - ω₀) / t. Since the body comes to rest (ω = 0) in 1 minute (t = 60 s), α = -2π / 60 = -π / 30 rad/s². Torque is given by τ = Iα, so τ = 2 × (-π / 30) = -π / 15 N·m.

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