Question

A circular gear turns 120 per hour. Through how many radians does it turn in a 24-hour day?

Answer 1

Number of radians in one revolution =  2π

Radians in 24 hours = 24 * 120 * 2π  =   18,095.57 radians

Answer 2

In a 24 hour day, the gear will turn 16π radians.

What is a radian?

'Radian is a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 57.3 degrees.'

According to the given problem,

Number of turns per hour = 120

Number of radians in a 24-hour day = $\frac{120}{360}$ × 2π × 24

                                                             = $\frac{2\pi }{3}$ × 24

                                                             = 16π

Hence, we can conclude, in a 24 hour day, the circular gear will make 16π turns.

Learn more about radians here: https://brainly.com/question/7721249

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