Question

1. a satellite orbiting earth 340 km above the surface makes one complete revolution every 90 minutes. the radius of earth is approximately 6370 km. the angular speed of the satellite is: a. \\(\frac{\pi}{5400}\\) rad/s b. \\(\frac{\pi}{2700}\\) rad/s c. \\(\frac{\pi}{90}\\) rad/s d. \\(\frac{\pi}{45}\\) rad/s

Explanation:

Step1: Recall the formula for angular speed

Angular speed \(\omega\) is given by the formula \(\omega=\frac{\theta}{t}\), where \(\theta\) is the angle rotated and \(t\) is the time taken. For one complete revolution, \(\theta = 2\pi\) radians.

Step2: Convert time to seconds

The satellite makes one revolution every 90 minutes. We know that 1 minute = 60 seconds, so \(t = 90\times60= 5400\) seconds.

Step3: Calculate angular speed

Substitute \(\theta = 2\pi\) and \(t = 5400\) into the formula \(\omega=\frac{\theta}{t}\). So \(\omega=\frac{2\pi}{5400}=\frac{\pi}{2700}\) rad/s.

Answer:

B. \(\boldsymbol{\frac{\pi}{2700}}\) rad/s