please solve example 10.9. based on Algbra and trig Angular momentum Using the d
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please solve example 10.9. based on Algbra and trig
Angular momentum Using the definition of angular momentum, L = I_omega, the torque equation can be expressed in the form in terms of impulse due to individual torques. If the external torques add up to to zero there is no change in angular momentum and we have the conservation of angular momentum L_1i + L_2i = L_1f + L_2f. Lecture-Example 10.9: A merry-go-round, in the shape of a disc, is free to rotate (without frict ion) about its symmetry axis. (It has mass M = 100.0, kg, radius R = 2.00 m, and moment of inertia I = 1/2 MR^2.) A kid (mass m = 25.0 kg) walks from the outer edge of the disc to the center. If the angular speed of the merry-go-round was omega_i = 0.30rev/s when the kid was at the outer edge, what is the angular speed of the merry-go-round when the kid is at the center? Use conservation of angular momentum. L_i^disc + L_i^kid = L_f^disc + L_f^kid, to derive omega_f = (1 + 2m/M)omega_i.Explanation / Answer
L disc + Lkid = L disc + Lkid
MR^2/ 2 *Wi + m/R^2 * Wi = MR^2/ 2 *Wf + 0
Wf = {MR^2/ 2 *Wi + m/R^2 * Wi} / MR^2/ 2
Wf = ( Wi + 2m/M *Wi )
Wf = ( 1+ 2m/M) Wi .....................................proved now just plug the values
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