A uniform bar has two small balls glued to its ends. The bar is 2...

Question

A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis (d) parallel to the bar and 0.500 m from it.

Accepted Answer

Hello everyone. So in this problem we have two tiny spheres which are welded into a regular metallic antenna. His fears have a mass of 25 g each. Whereas the antenna is one m long and it has a mass of 250 g. Assuming that the size of the spheres is small enough compared to the length of the antenna, calculate the Moment of inertia of this system about a fixed-axis parallel to the antenna. With the distance between the access and the antenna is 15 cm. So we have two metallic spheres. They're connected by a metallic container And the antenna is one m long. And the intent the massively antenna Is equal to 250g Which divided by 1000 g. To get kg. We get .250 kg and the mass of each ball Is equal to g which we convert to kg again by dividing 1000 g you get .025 kg. We want to find the moment of inertia about a peril access. But the distance between the parallel access and metallic antenna is 15 centimeters which divided by 1000 cm Is .015 m. So by the parallel axis theorem, which we recall is I prime is equal to I of the center of mass plus m Total times are totals Where R is the distance from the centre of mass to the parallel axis which is equal to this .015 m. I am. The center of mass is parallel to the metallic antenna. And since it is parallel to the metallic antenna and antenna and the distance between each point mass Is equal to zero. And I see em Must also be equal to zero if it is rotating about its center of mass access parallel to these balls. So we see the ICM is zero and that I prime is equal to m. Total times are t squared. So we can simply calculate the total mass by just adding up all of the mass components of this apparatus. So I prime is equal to, we have the mass of the antenna Which is .250 kg. And we have two balls Which are .025 kg each. And we just simply multiply this by the distance from the center of mass to the parallel axis 015 m Squared. And then calculating this, we get that I prime because you put 6.75 times 10 to the negative three describe gives us answer choice of this house.

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