(7%) Problem 14: A playground rev/s. with a mass of 105 kg and a radius of 1 9 m

Question

(7%) Problem 14: A playground rev/s. with a mass of 105 kg and a radius of 1 9 m is rotating with a frequency of 0 S4 Randomized Variables mi 105 kg m2= 21 kg a).-0.54 rev/s r=1.9 m What is the magnitude of its angular velocity, in radians per second, after a 21 kg child gets onto i by grabbing ts outer edge? The child is initially at rest. cof = 0451 Deductions 95% Potential cosO cotanO asinO acosO atan0 acotansinh0 Attempts remaining (5% per attempt) detailed view tanh cotanhBACKSPACE 0 END Degrees Radians I give up! Hint Submit Hits: 2% deduction per hint. Hints remaining: 2 All content © 2017 Expert TA,LLC

Explanation / Answer

Initial moment of inertia (solid disk) Ii = 0.5*M*r^2 = 0.5*105*1.9^2 = 189.525 kg.m^2

Initial angular velocity i = 0.54*2pi rad/s = 3.39 rad/s

Angular momentum = Ii*i = 643.302 kg.m^2/s = constant

Child moment of inertia (point mass) = m*r^2 = 21*1.9^2 = 75.81 kg.m^2

Final moment of inertia If = 189.525 + 75.81 = 265.335 kg.m^2

So final speed is f = 643.302 / 265.335 rad/s = 2.4244 rad/s

or 2.4244 / 2pi = 0.385 rev/s

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