While sitting in physics class one day, you begin to ponder the workings of the

Question

While sitting in physics class one day, you begin to ponder the workings of the analog clock on the classroom wall. You notice as the hands sweep in a continuous motion that there are exactly 41 minutes left in class. A) Through what (in radians) will the second hand turn before the end of the class? B) Through what (in radians) will the minute hand sweep before the end of class? C) Through what angle (in radians) will the hour hand sweep before the end of class? D) calculate the angular velocity of the second hand in radians per second. E) Calcualte the angular velocity of the minute hand in radians per second. F) Calculate the angular velocity of the hour hand in radians per second. G) Is the angular acceleration of the second, minute, and hours hand at the same time?

Explanation / Answer

A) 60 time minutes = 360 degree (or 2Pi radians) angle of rotation for the minute hand. But the second hand does 2Pi every minute. So answer is 41*2Pi = 82Pi radians

B) With info given in part 1, use 60 min = 2Pi rad as a conversion factor:

42 min * 2Pi rad / 60 min = 7Pi/5 rad

C) the hour hand makes one complete circle (2Pi rad) every 12 hours

and 1 hour is 60 minutes. so we need two factors:

42 minutes * (1 hour / 60 min) * (2Pi rad / 12 hour) = well, this is same as previous problem except we divide by 12, so we jump to the "almost final" answer:

42Pi/(30*12) rad = 7Pi/60 rad

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