The seconds hand of a clock is 6 cm long. Find the speed of its tip and the magnitude of the change in its velocity between two positions that are 90 degrees apart.

2pi & 0 mm/s
2sqrt(2) pi & 4.44 mm/s
2sqrt(2) pi & 2pi mm/s
2pi & 2sqrt(2) pi mm/s

Correct answer: 2pi & 2sqrt(2) pi mm/s

Solution

With omega = 2pi/60 and r = 60 mm, the tip speed is 2pi mm/s; at perpendicular positions the velocity change magnitude is sqrt(2) times the speed, i.e. 2sqrt(2) pi mm/s.

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