Question

The Earth rotates about its axis once every 23 hours, 56 minutes, and 4 seconds. Approximate the number of radians Earth rotates through in one second. (Rad)/Sec

A) 7.27 x 10^-5
B) 1.04 x 10^-4
C) 2.14 x 10^-4
D) 3.22 x 10^-4

Answer 1

The Earth rotates through approximately 7.27 x 10^-5 radians every second, which is calculated by dividing 2π radians by the total number of seconds in one rotation (86164 seconds).

Step-by-step explanation:

The student is asking how many radians the Earth rotates through in one second. Since one full rotation of the Earth is equivalent to 2π radians, and the Earth takes 23 hours, 56 minutes, and 4 seconds for one rotation, we can calculate the rate in radians per second. The total time in seconds for one rotation is 23 × 3600 + 56 × 60 + 4 = 86164 seconds.

Therefore, the rate of Earth's rotation in radians per second is 2π radians divided by 86164 seconds, which equals approximately 7.27 x 10^-5 radians/second (Option A).