4 a. What is the period of rotation of Earth in seconds? b. What is the angular

Question

4 a. What is the period of rotation of Earth in seconds?

b. What is the angular velocity of Earth?

c. Given that Earth has a radius of 6.4 x 106 at its equator, what is the Linear velocity at Earth's surface.

19. A rotating space station is said to create " artificial gravity" - a loosely - defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non - rotating space environments. If the space station is 200 m in diameter, what angular velocity would produce an " artificial gravity" of 9.80 m/s squared at the rim?

5. Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration or both when

a) The plate starts to spin?

b) The plate rotates at constant angular velocity?

c. The plate slows to a halt?

(PLEASE SHOW ALL WORKING AND SOLUTIONS)

Explanation / Answer

4a.The actual value of the period of rotation of earth is 23 hours 56 minutes and 4 seconds. This happens because a solar day is longer than a sidereal day. While the earth rotates, it also moves around the sun in the interval from one day to another.

b.The Earth rotates at a moderate angular velocity of 7.2921159 × 10-5 radians/second

c. Given: Earth's radius = 6.4 x 106m
           Angular velocity = 7.3 x 10-5rad/s
thus, the linear speed of any point on the earth's surface at the equator due to earth's rotation is, V = r = 6.4 x 106 x 7.3 x 10-5m/s = 470 m/s

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