# Gravity and Angular acceleration

**1. The problem statement, all variables and given/known data**

There is strong evidence that Europa, a satellite of Jupiter, has a liquid ocean beneath its icy surface. Many scientists think we should land a vehicle there to search for life. Before launching it, we would want to test such a lander under the gravity conditions at the surface of Europa. One way to do this is to put the lander at the end of a rotating arm in an orbiting earth satellite.

If the arm is 5.25m long and pivots about one end, at what angular speed (in rpm) should it spin so that the acceleration of the lander is the same as the acceleration due to gravity at the surface of Europa? The mass of Europa is 4.8E22kg and its diameter is 3138 km.

[itex]\omega [/itex] =_____rpm

**2. Relevant equations**

[itex]v=\omega r [/itex]

[itex]\frac{GMm}{R^2}=a[/itex]

[itex] T = \frac{2\pi}{\omega} [/itex]

**3. The attempt at a solution**

[itex]\frac{GMm}{R^2}=a[/itex]

[itex]\frac{mv^2}{R}=ma[/itex]

[itex]\frac{\omega^2R}{a}[/itex]

[itex]\omega=\sqrt{\frac{a}{R}}[/itex]

[itex]\omega=\sqrt{\frac{GM}{R_{europa}^2*R_{sat}}}[/itex]

[itex] \frac{60\omega}{2\pi}[/itex] = x rpm

Edit: Figured out the problem. The diameter of Europa is given in Km, you have to convert it to meters. Stupid Mastering Physics…

Apparently that’s not right though??

http://ift.tt/1q18djC

## Leave a comment