The minute hand of a wall clock measures 14 cm from its tip to the axis about wh

Question

The minute hand of a wall clock measures 14 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the (a) magnitude and (b) angle from a quarter after the hour to half past, 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 from the +x direction (to the right, or 3 o'clock).

Explanation / Answer

Here ,

a)

for quater after the hour to half past ,

theta = pi/2 radians

displacement = sqrt(R^2 + R^2)

displacement = sqrt(0.14^2 + 0.14^2)

displacement = 0.20 m

b)

angle = 180 + arctan(R/R)

angle = 225 degree

the angle of displacement is 225 degree

c)

displacement = 2 * R

displacement = 2 * 0.14

displacement = 0.28 m

d)

minute hand moves from half past to hour

angle = 90 degree with +ve x - axis

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