A solid cylinder of mass 2 kg and radius 4 cm spins about its axis at 3 rpm. Find the torque needed to bring it to rest after 2π revolutions.
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A solid cylinder of mass 2 kg and radius 4 cm spins about its axis at 3 rpm. Find the torque needed to bring it to rest after 2π revolutions.

G1 Physics · Accepted Answer

Step 1: Initial ω₀=3×2π/60=π/10 rad/s. Step 2: Angular displacement equals 2π revolutions =4π² radians. Step 3: Using 0=ω₀²+2αθ yields |α|=(π²/100)/(8π²)=1/800 rad/s². Step 4: Cylinder inertia I=½MR²=0.0016 kg·m². Step 5: Braking torque magnitude τ=I|α|=2×10⁻⁶ N·m. Final answer: D — 2×10⁻⁶ N·m.