Question:
In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has radius \(10\,\text{m}\), then to achieve centripetal acceleration at a point on circumference as \(10\,\text{ms}^{-2}\), its angular speed is
In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has radius \(10\,\text{m}\), then to achieve centripetal acceleration at a point on circumference as \(10\,\text{ms}^{-2}\), its angular speed is
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For circular motion, centripetal acceleration is \(a_c=\omega^2r\). Use this formula directly when radius and acceleration are given.
Updated On: Jun 26, 2026
- \(1\,\text{rad s}^{-1}\)
- \(10\,\text{rad s}^{-1}\)
- \(1\,\text{revolution s}^{-1}\)
- \(10\,\text{revolution s}^{-1}\)
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The Correct Option is A
Solution and Explanation
Step 1: Use the formula of centripetal acceleration.
Centripetal acceleration is given by \[ a_c=\omega^2r \] where \[ \omega \] is angular speed and \[ r \] is radius.
Step 2: Substitute the given values.
Given, \[ a_c=10\,\text{ms}^{-2} \] and \[ r=10\,\text{m} \] So, \[ 10=\omega^2(10) \] \[ \omega^2=1 \] \[ \omega=1 \] Since angular speed is positive, \[ \omega=1\,\text{rad s}^{-1} \]
Step 3: Final conclusion.
Hence, the angular speed of the satellite is \[ \boxed{1\,\text{rad s}^{-1}} \]
Centripetal acceleration is given by \[ a_c=\omega^2r \] where \[ \omega \] is angular speed and \[ r \] is radius.
Step 2: Substitute the given values.
Given, \[ a_c=10\,\text{ms}^{-2} \] and \[ r=10\,\text{m} \] So, \[ 10=\omega^2(10) \] \[ \omega^2=1 \] \[ \omega=1 \] Since angular speed is positive, \[ \omega=1\,\text{rad s}^{-1} \]
Step 3: Final conclusion.
Hence, the angular speed of the satellite is \[ \boxed{1\,\text{rad s}^{-1}} \]
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