You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.400 kg. (b) One of your engineers has proposed to reduce the moment of inertia by bending the rod at its center into a V-shape, with a 60.0o angle at its vertex. What would be the moment of inertia of this bent rod about an axis perpendicular to the plane of the V at its vertex?

Video transcript

Hello. Everyone in this problem you oversee projects for a business that produces goods. A thin uniform rod measuring 60 centimeters in length and weighing 4.4 kg is one of the machine parts being assembled on the assembly line. One of your engineers has suggested that you bend the rod at its center into a V shape with a 30 degree angle at it's vertex. In order to lessen the amount of a moment of inertia. What would this bent broads moment of inertia be at its vertex which is an axis perpendicular to the plane of the beef. So we know that the axis of rotation is perpendicular to the plane of the V. That there is a 30° bend And that the uniform Rod measures 60 cm in total length and it weighs .4 kg. So you can start by drawing a simple schematic and we know that the axis of rotation is perpendicular to me. So looking from the top, we see that there is a v. And it was a 30° bend. But since it is perpendicular we could take a side view of this set up and we can notice that if the axis of rotation is perpendicular, it essentially looks like two rods with them over to And L over two buzz length and mass rotating about this Access of rotation. So the 30° bend actually does not matter in this case, since the axis of rotation is perpendicular to the plane. So we recall that the a moment of inertia simply for a rod about a perpendicular axis was 1/ and square. And in this case we have this one half rod and we have a second half rod rotating about this axis. So we can calculate I as 1/ and over to Times L over two squared Was another 1/3. Em over to over two square And now we know that the total mass is .4 kg. The total length is 60 centimeters, which converted to leaders Is just .6 m. So we have L. We have and then we can make substitutions to now find the moment of inertia. So on the third programs over to, Oh it is .6 m squared and then we have the second turn. And when calculated, this gives us an answer of 0.032 kg times m square. His answer choice C hope this helps have a great day.