a) Since the earth rotation is uniform, the instantaneous velocity is given by the length l of a path of a point at the equator divided by the time t during which this path is passed. Taking the circumference of the equator as a path, we have l = 2πr, where r is the radius of the earth. This path is passed in 24 hours, which constitutes 86400 seconds. The velocity is v = 2πr/t ≈ 465 m s–1.
Answer: 465 m s–1.
b) The centripetal acceleration is given by the formula a = v2/r. Hence, a = (465 m s–1)2/(6.4 × 106 m) ≈ 3.4 × 10–2 m s–2.
Answer: 3.4 × 10–2 m s–2.