Question

What is the angular speed about the rotational axis of the Earth for a person standing on the surface? a. 7.3' 10-5 rad/s b. 3.6' 10-5 rad/s c. 6.28 '10-5 rad/s d. 3.14' 10-5 rad/s

Answer 1

The angular speed of the Earth for a person on the surface is approximately 7.3 x 10^-5 rad/s, which is found by dividing 2π by the number of seconds in a day (86,400).

Step-by-step explanation:

The angular speed about the rotational axis of the Earth for a person standing on the surface can be calculated by considering the fact that the Earth completes one rotation every 24 hours. To convert this period into seconds, we multiply 24 hours by 60 minutes per hour and 60 seconds per minute which gives us 24 * 60 * 60 = 86,400 seconds per rotation.

Angular speed, ω, is defined as the angle rotated per unit time. The Earth rotates through 2π radians (which is one complete rotation) in one period (T). Therefore, ω = 2π / T. Substituting in our period in seconds, we get ω = 2π / 86400. Calculating this gives us an angular speed of approximately 7.27 x
`10^(-5)` rad/s.

Therefore, the correct answer is a. 7.3 x
`10^(-5)` s, which is closest to the actual calculated value.

Answer 2

The angular speed of a person standing on Earth's surface is approximately 7.27 × 10^-5 rad/s, which corresponds to option (a) 7.3 × 10^-5 rad/s.

Step-by-step explanation:

The angular speed of a person standing on the surface of the Earth can be calculated based on the period of rotation of the Earth. The Earth completes one rotation every 86,400 seconds (which is 24 hours), and a full rotation corresponds to 2π radians (360 degrees).

Therefore, to find the angular speed ω (in radians per second), we can use the formula ω = Θ/t, where Θ is the angle in radians (2π for one full rotation) and t is the time period in seconds.

ω = 2π radians / 86,400 seconds = approximately 7.27 × 10^-5 rad/s, which is closest to option (a) 7.3 × 10^-5 rad/s.