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Home » \( \theta = 30^\circ \) (angle) - Crosslake

\( \theta = 30^\circ \) (angle) - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Standard: minute hand rotates 720 times in 24 hours (1 full rotation every hour, but scaled). Wait — correct: standard minute hand completes 720 rotations in 24 hours? No — 1 rotation per hour → 24 rotations in 24 hours. Contradiction.

📌 Clarify: In 12 hours, minute hand completes 12 rotations. So in 24 hours: 24 rotations. But question says 720 — clearly inconsistent. Re-analyze:

📌 "Minute hand completes 720 rotations in 24 hours" — this suggests a hyper-fast model or scaled system.

📌 But standardly, minute hand: 1 rotation per 60 minutes → 24 rotations per day. 720 is 30 days. So perhaps it's not standard time — or more likely, misinterpretation.

📌 Wait: perhaps it's not a standard clock. The gear model rotates 720 times for the minute hand in 24 hours. Then ratio of teeth tells motion? But gear ratio is based on teeth: linear speed ratio = T_hour / T_minute.

📌 But we are told minute gear has 72 teeth. Let T_hour be unknown. In standard gearing, rotations per hour:

📌 Minute hand: 720 rotations / 24 days = but per hour: in 24 hours, 24 rotations. So per hour: 1 rotation.

📌 So minute gear rotates 1 time per hour → 24 times in 24 hours. But question says 720 — contradiction.

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