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Solution to Exercise 7
(a) The second hand goes all the way around once (moves 360 degrees) in 1 minute (60 seconds), so it travels at speed v = 360/60 = 6 deg/s. The minute hand goes around once in one hour (60 * 60 = 3600 s), so it travels at v = 360/3600 = 0.1 deg/s. The hour hand goes around once in twelve hours (12 * 3600 = 43200 s), so it travels at v = 360/43200 = 0.0083 deg/s. (b) The tip of the hour hand travels a circle with circumference C = 2?r = 2 * 3.14 * 0.1 m = 0.628 m, and it makes that circuit in twelve hours = 12 * 3600 = 43200 s. So its linear velocity is v = 0.628/43200 = 0.0000145 m/s In other units, one mile is about 1600 m and one hour is 3600 s, so v = (0.0000145 m/s) * (3600 s/hr) / (1600 m/mi) = 0.000033 miles/hr. Not very fast... but it gets there, day after day, night after night. |