Question

Assuming that a day is exactly 24 hours long (and neglecting the motion of the Earth around the Sun, which adds a small correctionto this):

(a) What is the angular velocity of an object resting on the surface of the Earth, as seen from a true inertial (non-spinning) frame? (Give your answer in rad/s. You’ll want to use scientific notation here.)

(b) The radius of the Earth is approximately 6.37×106m. What is the centripetal acceleration of an object rest-ing on the surface of the Earth at the equator? (Give magnitude and direction.)

(c) What is the centripetal acceleration for an object resting on the surface of the Earth at a latitude of 60◦north,as in the figure? (Magnitude only; see next question for direction!)

(d) In what direction does the centripetal acceleration point for the object in part

(c)? Draw an arrow on the figure showing this acceleration.

(e) What two forces acting on this object must be added, as vectors, so as to yield this acceleration? NS60º Side view of the Earth as it spins around the vertical (North-South) axis. The object (black dot) spins with it.

Note: If you answered parts (d) and (e) correctly, you may be feeling a little uneasy now. If you think long enough about it, it may seem that those answers are incompatible. What do you think may be the solution? (Hint: isthe Earth really shaped like a perfect sphere?)

Answer 1

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