arth rotates ance per day about an ais pansing through the north and south pokes

Question

arth rotates ance per day about an ais pansing through the north and south pokes, an ads thut ts perpmdicdar to the hane of the equt acceleration of a person situated at each of the foliowing. Auing the earth i a sphe with a a of 63x 49.0 north ofthe nms e an amusement park there is a ride in which cylindrically shaped chambers spin around a central asesit in seats facing the ails, ther hacks at a speed eels a 590-N orce pressing against His back. What is the radus of a chamber? Sedion 5 3 As an aid in working this prelem cosult Comoept Simulation 52 ourve whut is the masmum speed which car can etae the curve

Explanation / Answer

1)

angular velocity is

w = 2pi / T here T is 1 day

w = (2pi / day) x (1 day / 24 h) x (1 h / 60 min) x (1 min / 60 s)

w = 7.272 x 10^-5 rad/s

a)

V = Re*w

V = 6.38 x 10^6 x 7.272 x 10^-5

V = 464 m/s

the acceleration of the person situated at equator is

a = w^2 x Re

a = (7.272 x 10^-5)^2 x 6.38 x 10^6

a = 0.0337 m/s^2

b)

At altitude, radius is

R = Re x cos(49)

R = 6.38 x 10^6 x cos(49)

R = 4.186 x 10^6 m

a = w^2R

a = (7.272 x 10^-5)^2 x 4.186 x 10^6

a = 0.0221 m/s^2

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