Question

The Moon (radius = 1.74 X 10⁴ m) rotates once on its axis in 27.3 days.

What is its period of rotation, frequency of rotation, and linear speed?

a. 2.36 X 10⁶ sec, 2.66 X 10⁻⁶ rad/s, 4.63 m/s
b. 3.01 X 10⁶ sec, 2.56 X 10⁻⁵ rad/s, 4.91 m/s
c. 2.09 X 10⁷ sec, 3.5 X 10⁻⁶ rad/s, 5.05 m/s

Answer 1

The Moon's period of rotation is 2.36 × 10⁶ seconds, with a frequency of 4.24 × 10⁵ Hz and a linear speed of approximately 4.63 m/s at the equator.

Step-by-step explanation:

The Moon's period of rotation can be calculated by converting days into seconds. Since we know the Moon rotates once on its axis in 27.3 days, we can calculate its period (T) in seconds as T = 27.3 days × 24 hours/day × 3600 seconds/hour = 2.36 × 10⁶ seconds. The frequency of rotation, which is the inverse of the period, would be f = 1/T = 1/(2.36 × 10⁶ seconds) = 4.24 × 10⁵ Hz. To find the linear speed (v) at the equator, we use the formula v = 2πr/T, where r is the radius of the Moon and T is the period. Substituting the given values, we get v = 2π × (1.74 × 10⁴ m) / (2.36 × 10⁶ s) which approximately equals 4.63 m/s. Therefore, the correct answer choice is a. 2.36 × 10⁶ sec, 4.24 × 10⁵ Hz, 4.63 m/s.