Question

The figure shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0.6 m, its inner radius R1 is R2/2, its mass M is 7.3 kg, and the mass of the crossbars at its center is negligible. It initially rotates at an angular speed of 7.7 rad/s with a cat of mass m M/4 on its outer edge, at radius R2. By how much does the cat increase the kinetic energy of the cat-ring system if the cat crawls to the inner edge, at radius R1? Units Number

Answer 1

moment of is Tring inertia of Hollow ding Iring = M(R? + R² Initial When - eat is at outer edge of Cent. then moment of inertia theast yp R2 Teat); - Man Alesk Total moment of I futical - inentia Tring - in initial Icat a I Tinitial - M (Rith 2 + M ² given to (hey = 0.6m | R, = 0.3 m/ R = R = 0 [M=#sky)

Inital = 7.3 (0.6²+ 0.32 703 (0.62 Iinitial - 1.6425+ 0.657 I'mital - 2.299 kg-m² final When Cat of inertia is einer edge then moment (I cat) = MR? Total moment of intentia in final I final - Iering + Icat) I final = M(R+R) + M R? - I final - 7.3 (0.8+ 0.62) + 7:3 (037² - - 1.6425+ 0.16425 Ifinal = 1.806 kg-m2

conserve. Angular moment is - Li- t Tinical wo - given (Wi- 707 sad/s I final of 2.299 x 7.7 1.806xWf they = Ice Bradt Increase system the kinetic energy of cat sing is equal to I DKE = KE - KE; LAKE = 1 If we 2 - I I; Wp " 2 - AKE = _JxL+804x19.9342- 4 $2,299268777 AKE = 86.724-68.153 Increase the AKE = 18.57 | 1 Kinetic energy L of catering-systen