### Artificial Gravity in SpacecraftSpacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s². #### Problem Statement:If a giant space station with a mass of \(2.8 \times 10^{17}\) kg and a radius of \(5.05 \times 10^6\) m wanted to create that type of artificial gravity, what angular velocity would be required?#### Answer Choices:- \(1.39 \times 10^{-3} \text{ rad/s}\)- \(7030 \text{ rad/s}\)- \(4.95 \times 10^7 \text{ rad/s}\)- \(1.94 \times 10^{-6} \text{ rad/s}\)To solve this, we can use the formula for radial (centripetal) acceleration \(a_r = \omega^2 r\), where \(\omega\) is the angular velocity and \(r\) is the radius.Given:- Radial acceleration, \(a_r = 9.8 \text{ m/s}^2\)- Radius, \(r = 5.05 \times 10^6 \text{ m}\)Rearranging the formula to solve for \(\omega\):\[ \omega = \sqrt{\frac{a_r}{r}} \]Substituting the given values:\[ \omega = \sqrt{\frac{9.8}{5.05 \times 10^6}} \]Performing the calculation:\[ \omega \approx 1.39 \times 10^{-3} \text{ rad/s} \]Thus, the correct answer is:- \(1.39 \times 10^{-3} \text{ rad/s}\)

The equation for the magnitude of the radial acceleration is given by,

Spacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s2. If a giant space station with a mass of 2.8 x 1017 kg and a radius of 5.05 x 106 m wanted to create that type of artificial gravity, what angular velocity would be required? O 1.39 x 103 rad/s 7030 rad/s 4.95 x 107 rad/s O 1.94 x 10-6 rad/s

Spacecraft could create a type of artificial gravity by spinning fast enough to create a radial acceleration equal to 9.8 m/s2. If a giant space station with a mass of 2.8 x 1017 kg and a radius of 5.05 x 106 m wanted to create that type of artificial gravity, what angular velocity would be required? O 1.39 x 103 rad/s 7030 rad/s 4.95 x 107 rad/s O 1.94 x 10-6 rad/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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