Consider a cylindrical turntable whose mass is M and radius is R, turning with a

Question

Consider a cylindrical turntable whose mass is M and radius is R, turning with an initial angular speed ?1 (a) A parakeet of mass m, after hovering in flight above the outer edge of the turntable, gently lands on it and stays in one place on it, as shown below. What is the angular speed of the turntable after the parakeet lands? (Use any variable or symbol stated above as necessary.) wf= ? (b) Becoming dizzy, the parakeet jumps off (not flies off) with a velocity relative to the turntable. The direction of is tangent to the edge of the turntable and in the direction of its rotation. What will be the angular speed of the turntable afterwards? Express your answer in terms of the two masses m and M, the radius R, the parakeet speed and the initial angular speed ?1. (Use any variable or symbol stated above along with the following as necessary: v for vector v.) wf= ?

Explanation / Answer

L=mvr+I? I(turntable)=.5MR^2 I=?mr^2 ?f= ?1 + 2m?1/M -2mv/(MR) .5MR^2?1 +mR^2?1= .5MR^2?f +mvR so .5MR^2?1 +mR^2?1 -mvR = .5MR^2?f and (.5MR^2?1)/(.5MR^2) +(mR^2?1)/(.5MR^2) - (mvR)/(.5MR^2) = ?f right? which means that ?1 +2(m?1)/M - 2(mv)/(MR) = ?f

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