1. Consider the centripetal acceleration due to the earth's spin for a CWRU student sitting in Strosacker auditorium.

[The radius of the earth is R = 6378.1 km, Cleveland's latitude (angle from the equator) is 41.4994° N and a day is about 86400 seconds long.]

A. In what direction does this acceleration point with respect to a line drawn ‘vertically down'; i.e in the direction an object falls if released?

B. What is the magnitude of thiscentripetal acceleration?

You'll hopefully find that |acentripetal| is much less than |g|.

C. What force supplies this centripetal acceleration?

D. What are the angular and tangential acceleration due to earth's rotation for this student?

E. If you were standing at the equator instead of sitting in Cleveland (to make this question easier), how fast would the earth have to spin before gravity could no longer hold you onto the surface of the planet? Provide your answer in terms of angular velocity with numbers and units) but also in terms of the period T (which is currently 1 day = 86400 seconds).