The minute hand of a wall clock measures 17 cm from its tip to theaxis about whi

Question

The minute hand of a wall clock measures 17 cm from its tip to theaxis about which it rotates. The magnitude and angle of thedisplacement vector of the tip are to be determined for three timeintervals. What are the (a) magnitude and(b) angle from a quarter after the hour to halfpast, the (c) magnitude and (d)angle for the next half hour, and the (e)magnitude and (f) angle for the hour after that?Give all angles as positive values measured counterclockwise fromthe +x direction (to the right, or 3 o'clock).

Explanation / Answer

First, let's define the location of our polar plot: Theposition 0 (at any angle) is on the center of the clock, the axlewhere all hands are attached. Second, it is defined that the3 o'clock position 0 degrees, and clockwise is positive. Lastly, we are given the length of the minute hand at 17 cm. That value will never change, and is the amplitude of allanswers.
a, b) at half past, the magnitude (relative to 0) isunchanged at 17; the angle has moved from 0 to 90 degrees.
c, d) The next half hour, the minute hand has moved from 6 to12. The magnitude is still 17, the angle is 270.
e,f) The minute hand has made one additional rotationfor an added 360 degrees. It is back at 12 o'clock. So,you could consider this point as magnitude 17 angle 630, which isright, but not a normal format for this answer as the angle is morethan 360. Even though the minute hand has moved through 630degrees, the normal answer is driven by its location, not how itgot there. This is at angle of 270 degrees.

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