Final answer:
The period of rotation of Earth is 24 hours, or 86,400 seconds, which is not represented by the options provided. The angular velocity of Earth is approximately 7.27×10^(-5) radians per second. The linear velocity at Earth's equator is approximately 465 meters per second.
Step-by-step explanation:
Period of Rotation of Earth
The period of rotation of Earth, which is the time it takes for the Earth to make one complete turn on its axis, is 24 hours. A day on Earth is often referred to as having 24 hours, but when expressed in seconds, it is equal to 86,400 seconds (24 hours × 60 minutes per hour × 60 seconds per minute). Therefore, the correct answer to the question is not provided in the options a) 23.5 s, b) 24.0 s, c) 24.5 s, or d) 25.0 s, because the period of rotation in seconds is much larger than any of those values.
The angular velocity (ω) of Earth is calculated by taking the ratio of 2π radians to the period of rotation (T), which is ω = 2π / T. Since T = 86,400 seconds, the angular velocity of Earth is approximately 7.27×10^(-5) radians per second.
The linear velocity (v) at Earth's surface at the equator can be found by using the formula v = ω * radius, where the radius (r) of Earth is about 6.4×10^6 meters. This gives a linear velocity of approximately 465 meters per second at Earth's equatorial surface.