Question

Please answer that question ASAP

1. Consider a disc and hoop both of the same mass M, radius R and thickness I. a) Explain why one of these objects has a larger moment of inertia (about an axis through the center of mass and perpendicular to the plane of the object) than the other. What effect does the thickness I have on the rotational inertia? b) Explain how the rotational inertia of the disc may be obtained by adding the rotational inertias due to a series of hoops. Write down an expression (integral) representing this sum over hoop inertias. c) Consider the rotational inertia of a hoop about an axis through its center of mass but lying in the plane of the hoop. Do you expect this expression to be greater than or less than MR'? Explain. dm d) Consider the rotational inertia of the disc about the same axis as in the previous question (c) Explain how the rotational inertia can be obtained by using one of three different methods: two of these employing rods, and the other hoops.

Answer 1

(a) General Expression for moment of hertia is Mg², which shows that moment of inertia depend directly on the distance of mass distribution from center, that's why moment of inertia of a sing (hoop) is more than that of e cise Thickness ť has no effect on rotational hertia. (6) mass of disc=M Radius =R So mass per unit area e- M p- AR

1 dic š supposed to be made up of this singe each having width de and choose one such ring of radius 'x' . area of ring da= aux de so mass of sing dm = PdA = A 2 2xxche 1 dm = 2M adu So moment of inertia of this ring is di = din x² = 2M xdu) x² = 2M ndhu so total M. I. & disc I = 12m x che (c) usni pexpeditlax axis theorem I'+I'= I = MR? 21'= MR² I'= 12MR² (It's less than MR) (d) for disc, again using perpendicular aris theorem I'+I'= I = MAS 21' = 2 MR² I'=1/MR?