Question

1. Imagine acoordinates ystem Oxyz attached to amerry-go-rounddisk,with its origin Oat the disk centre, with the x-axis instantaneously going through 3 o’clock, the y-axis through 12 o’clock (both in the horizontal plane of the rotating disk) and the z-axis vertically upwards. Unit vectors i, j, k, are along the x,y,z axes respectively. The merry- go-round is rotating at a constant rate of 0.5k rad/s. A person sitting on the disk located at 6 o’clock throws a ball horizontally towards 12 o’clock at a throwing speed of 2 m/s. Determine the Coriolis acceleration of the ball on leaving the person’s hands, in terms of the unit vectors i, j, k.

Answer 1

$\\V_{rel}=Velocity\:of\:ball\:relative\:to\:point\:on\:merry\:go\:around\\\\ Direction\:of\:V_{rel}=6^0\:clock\:to\:12^0\:clock=j\\\ \\Magnitude\:of\:V_{rel}=2m/s\\\\ V_{rel}=2\hat_{j}m/s\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:w=0.5\hat_{k}$

$\\Coriolis \:accelaration=2\:(w\:\times v_{rel})\\\\\ \:Coriolis \:accelaration=2(0.5\hat{k}\:\times2m/s\hat{j})\\\\ Coriolis \:accelaration=2(-1\hat{i})\\\\ Coriolis \:accelaration=-2m/s\:\hat{i}$