A thin uniform rod has a length of 0.500 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.400 rad/s and a moment of inertia about the axis of 3.00 * 10-3 kg/m^2. A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of the rod. When the bug has reached the end of the rod and sits there, its tangential speed is 0.160 m/s. The bug can be treated as a point mass. What is the mass of (a) the rod;

Video transcript

Everyone in this problem. We have a uniform rod of length 0.8 m. Okay, fixed to a massless axle on one of its ends, such as its rotational axis is perpendicular to its length. The rods moment of inertia about the axle. 0.41 kg meter squared. The Rod is rotating at 1.4 radiance per second. When a remote controlled movable mass slides from very close to the axle to the opposite end of the Rod. The mass has a linear speed of 0.98 m/s when located at the opposite end. And were asked to determine the mass of the rod. Okay, we're told that we can treat that mass as a particle. Alright, so let's just draw a little diagram. Okay, we have this axis here and our rod which is rotating perpendicular early. So it's going to be rotating about this axis here. And the Rod is 0.8 m long. And let's just write out some of the other information. So again the mat or the length of the Rod is 0.8 m. Okay, its moment of inertia I equal to 0. kg meter squared. We're trying to find the mass. So let's start with the information we have here. Okay, before we get into the information about this movable mass, let's see what we can figure out just from the information about the rod. Now we're told the rods moment of inertia. And let's recall that the moment of inertia. I for a rod like this, it's rotating about one end perpendicular lee to its length is going to be equal to M. L squared over three. And again you can look this up in a table in your textbook or that your professor provided for the moment of inertia of this particular shape or object. Well, if we look at this, we want to find the mass. M. Okay? We actually know the moment of inertia. I and we know the length L. So we can find the mass. Using this information alone. We don't even need to worry about that movable mass and all of that information. So let's go ahead and plug in our information and see what mass we get. So the moment of Inertia is 0. kilogram meter squared. Ok. And this is equal to the mass M times of length. 0.8 m all squared divided by three. Alright, so we're gonna multiply up the three. Then we get 0.123 kilogram meter squared is equal to m Times 0.64. And we get meters squared. Okay, So we get em When we divide the unit of meter square world cancel we get that M is equal to 0. kilograms. Okay? And so the mass of our rod is going to be 0.192 kg. And if we go back to our answer choices, we see that this is gonna be answer choice. D 0.192 kg. And I just want to make a note here before we go that this works because the moment of inertia we were given is a moment of inertia of the rod. Okay. If we were given the moment of inertia of the whole system, the rod and the mass, we would have to consider the movement of that mass. When we do our calculation. Okay. But because we were given the moment of inertia, just of that rod, we can do the calculation as we did it here. Ok. And we get the mass of the rod is 0.192 kg. Thanks everyone for watching. I hope this video helped see you in the next one.