What is the angular velocity of an automobile negotiating a curved path with a radius of 100m traveling at 36 km/hour, expressed as_______________?
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Answer: A. 0.1 radian/sec
Explanation
Converting speed from kilometers per hour to meters per second yields ten meters per second. Dividing the linear velocity by the circular path radius of one hundred meters gives zero point one radians per second. This calculation applies the fundamental kinematic relation between linear speed and angular velocity. Angular velocity measures the rate of change of angular displacement over time along a curved trajectory. Unit conversion requires multiplying kilometers per hour by five-eighteenths to obtain meters per second. Centripetal acceleration depends directly on the square of the angular velocity multiplied by the radius.
Highway design engineers calculate angular velocities to ensure safe speed limits on curved road alignments. Vehicle dynamics analysis requires precise angular velocity values to evaluate tire cornering forces. Railroad track banking angles are determined using the operational speeds and curve radii of trains. Option B overestimates the angular velocity by a factor of ten compared to the correct calculation. Option C represents an excessively high angular velocity that does not match the given speed and radius. Option D is mathematically incorrect and would imply unrealistic centripetal forces for normal vehicles.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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