<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta property="og:title" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<title>To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.</title>
$2.2.23.$ To create artificial gravity, two compartments of the orbital station (mass ratio $1 : 2$) were separated by a distance $R$ from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="2.2.23_1.png"
loading="lazy" width="230" />
<figcaption>
Velocities of the system
</figcaption>
</figure>
</center>
<p>
$$\sum\vec{R}_\text{external} = \vec{0}$$
$F_3$ - The force of gravity on the ground acting on an object of mass $m$<br>
$F_2$ - The force of gravity on a massive compartment<br>
$F_1$ - The force of gravity on the less massive compartment <br>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta name="description" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta property="og:title" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta property="og:title" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<meta property="og:description" content="To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.">
<title>To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.</title>
<title>To create artificial gravity, two compartments of the orbital station (mass ratio 1 : 2) were separated by a distance R from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.</title>
$2.2.23.$ To create artificial gravity, two compartments of the orbital station (mass ratio $1 : 2$) were separated by a distance $R$ from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.
$2.2.23.$ To create artificial gravity, two compartments of the orbital station (mass ratio $1 : 2$) were separated by a distance $R$ from each other and spun around their common center of mass. Determine the time of complete rotation of the compartments if, in a more massive compartment, the artificial gravity is half the force of gravity on the Ground.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="2.2.23_1.png"
<img src="2.2.23_1.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
Velocities of the system
Velocities of the system
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
$$\sum\vec{R}_\text{external} = \vec{0}$$
$$\sum\vec{R}_\text{external} = \vec{0}$$
$F_3$ - The force of gravity on the ground acting on an object of mass $m$<br>
$F_3$ - The force of gravity on the ground acting on an object of mass $m$<br>
$F_2$ - The force of gravity on a massive compartment<br>
$F_2$ - The force of gravity on a massive compartment<br>
$F_1$ - The force of gravity on the less massive compartment <br>
$F_1$ - The force of gravity on the less massive compartment <br>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
