Gravity on spaceship

Classical Mechanics Level 2

Imagine that you are living in an advanced spacefaring civilization. In order to create gravity inside the spaceship which resembles the gravitational pull of Earth, the spaceship is rotated. The spaceship is cylindrical with a radius of 100 meters.

At what angular velocity ( ( in rad/s ) \text{rad/s}) should the spaceship be rotated to generate a gravity of 1 g 1\text{ g} near its curved surface?

Assume g = 10 m/s 2 . g = 10 \text{ m/s}^2.


The answer is 0.316.

Amogh Rakesh by Amogh Rakesh , 20, India

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3 solutions

Parth Sankhe
Dec 15, 2018

Centripetal force should be equal to gravity on earth,

m ω 2 r = m g m\omega ^2r=mg

Putting r=100 and g=10,

ω = 1 √ 10 \omega = \dfrac {1}{√10}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Rehaan Irani
Dec 15, 2018

F = mrω²

F = mg

Therefore: mg = mrω²

g = rω²

g must be 10 m/s^2 in order to simulate gravity on Earth. We are also given the radius of 100m.

10 = (100)(ω²)

ω² = 1 10 \frac{1}{10}

ω = √( 1 10 \frac{1}{10} )

ω = 0.316 rad/s

2 Helpful 0 Interesting 0 Brilliant 0 Confused

You don't need forces, you only need kinematics. You need to remember that a t a n = v 2 r a_{tan} = \dfrac{v^2}{r} . First, you find v v , which is equal to ω ⋅ r \omega \cdot r . You then take v v and r r and plug them into the first equation to get our answer which is 1 10 \sqrt{\dfrac{1}{10}} .

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