Question

(a) what is the angular speed (in rpm) with which the earth spins on its axis? rpm (b) what is the angular speed (in rpm) with which the earth revolves around the sun? assume that the path is circular. rpm resources reading

Explanation:

Step1: Recall the formula for angular speed in rpm

The formula for angular speed \(\omega\) (in rpm) is \(\omega=\frac{\text{Number of revolutions}}{\text{time (in minutes)}}\)

Step2: Calculate for Earth's spin (part a)

• The Earth makes \(1\) revolution about its axis in \(T = 24\) hours. Convert hours to minutes: \(T=24\times60 = 1440\) minutes.
• Using the formula \(\omega=\frac{n}{t}\), with \(n = 1\) revolution, \(\omega_a=\frac{1}{1440}\approx0.000694\) revolutions per minute. Rounding to a reasonable number of significant - figures (since \(1\) and \(1440\) are exact in this context), \(\omega_a=\frac{1}{1440}\text{ rpm}\approx0.000694\text{ rpm}\)

Step3: Calculate for Earth's revolution (part b)

• The Earth makes \(1\) revolution around the Sun in \(T = 365\) days. Convert days to minutes: \(T=365\times24\times60=365\times1440 = 525600\) minutes.
• Using the formula \(\omega=\frac{n}{t}\), with \(n = 1\) revolution, \(\omega_b=\frac{1}{525600}\text{ rpm}\approx1.90\times 10^{-6}\text{ rpm}\)

Answer:

a. \(0.000694\) rpm
b. \(1.90\times 10^{-6}\) rpm