A Gyroscope on the Moon. A certain gyroscope precesses at a rate of 0.50 rad/s when used on earth. If it were taken to a lunar base, where the acceleration due to gravity is 0.165g, what would be its precession rate?

Video transcript

Everyone welcome back in this problem. We have a spacecraft traveling from Earth to Mars and it uses a gyroscope to maintain its orientation and angular velocity and we want to determine what the procession rate of the gyroscope is near Mars's surface and we're told that the procession right near Earth's surface is one radiant per second and that the surface gravity of Mars is 38% of the surface gravity on earth. Now let's recall the precession rate omega on earth. Hey, this is given by M. G. And here we're talking the gravitational acceleration on Earth. So we'll call it G. Earth times are over. I oh my God. And we know that this is equal to one radiant per second. Okay, that's the information we were given in the problem. And when we're talking about the procession rate on MArs's surface. Okay, we're going to be looking at omega mars, we're talking about the gyroscope. We have again M. G. Now in this case, G we're talking about the surface of MArs so we're gonna have the gravitational acceleration of MArs. Hey, we have our and then we have divided by I omega. Okay, look at these equations. The M the are the of the omega are the same. It's the same Gyroscope. So all of those quantities will be the same. Okay, so the only thing that has changed is this G MArs. So let's fill in the information. We can about G mars. Okay, what do we know? Well we know that the gravitational acceleration of MArs is 38% of that on Earth. Okay, so we can write this is 0.38. Okay. 38% of the gravitational acceleration on Earth. G Earth times are all divided by I omega. If we pull this 0.38 out in front. Okay. It's a constant. It can be multiplied in front. We have em G. Earth are over. I Omega. Okay. And you might recognize this. Well this is the equation we had above for the procession rate on Earth. Okay so this is just going to be 0. times they go mega on Earth. Well what was that value? 0.38 times one radiant per second. Okay and this is going to give us a procession rate on mars. Omega mars Of 0.38 radiance for a second. That's going to correspond with answer B. I hope this video helped. Thanks everyone for watching