The carousel has radius 10m and rotates clockwise at speed 3m/s at the rim?

Question

A boy runs at speed 5m/s counter-clockwise on the rim of carousel (with respect to the carousel).

a) What is direction and magtidue of coriolis force acting on the boy?
b) What is angle (and direction) of inclination of the boy to the vertical?

Mass of the boy is 50kg

Answer 1

Coriolis acceleration (in the frame of the rotating disk) = -2 w X v (ref.), where X is the cross-product the 1st answer defines, and w is most definitely at right angles to v. According to the ref., "if the velocity is against the direction of local rotation, the acceleration is inward to the axis" (where the direction of rotation means the tangential direction).
a) With w = 0.3 and v = -2 the acceleration is 1.2 m/s^2 inward.
b) His inclination depends on his inertial acceleration. This is just the centripetal acceleration v^2/r = -2^2/10 = 0.4 m/s^2. His angle from the vertical = arctan(0.4/9.81).

Answer 2

Alexander,

Gaspard-Gustave de Coriolis would be most proud of you.

I believe he has said that his fictitious force Fc=-m W x V
Fc - coriolis force
m - mass of the boy
W- angular velocity of the carousel
V - velocity of the boy

x - designates vector product as in
WxV=|W||V| sin(a) a - angle between W and V

Since W is parallel to the boys speed V then W x V=0 and :Fc=0

Oh yea, please note that since the boy is 'staing' on the rim we can assume that his radial velocity is 0. If it was not then we can apply ...