When a particle is dropped from rest relative to the surface of the earth at a latitude , the initial apparent acceleration is the relative acceleration due to gravity g_rel. The absolute acceleration due to gravity g is directed toward the center of the earth. Derive an expression for g_rel in terms of g, R, ω, and , where R is the radius of the earth treated as a sphere and ω is the constant angular velocity of the earth about the polar axis considered fixed. Although axes x-y-z are attached to the earth and hence rotate, we may use Eq. 3 /50 as long as the particle has no velocity relative to x-y-z. 

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N y dB B grel R