Question

Example 9.2. In Figure 2, if the large ring, small ring and each of the spokes weigh 100 lb, 15 lb, and 20 lb, respectively, determine the mass moment of inertia of the wheel about an axis perpendicular to the page and passing through point A. Figure 2: Rings with spokes

Answer 1

Sof! Giveu ! Mass = loo eb a - Sol: Given: mass of larger ring (m) = 100 lb A mass of small ring (mi) = 15eb and mass a spokeo (m2) = 20 lb The wheel can be divided into different segunents : The Spokes which have a leugia q (4- a) ft - 3ft V B ound Center of mass localed A eq fit 3 f t = 2.5 ft from point o. can be grouped as ① : S ar a distand 2 J . - firstly we'll qu wheel compute mass moment q Cuentra about an axis perpendicular 20 3 2.2 32.2 32.2 to the page and passing through our to z toho(9* +8 [(.) 6] * max co? 10 = 84.94 slug. fth X 32.2 . - 84.92

The mass moment q arheel about ou a the page and passing parallel - anis theorean, luentia endicule ar to terrory "A usin C where I & Tot in d2 AG m= 100 & 8 (20 132:2 132.2 f 15 where, ma che + 8 699.) ma sosuou slug. slags 32 32 and da u ft. Thus, 1 I = 84.94+ (8.5oux = 221.58 slug

Approximately - I = 222 slug ft^2

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