A cylindrical turntable whose mass is M and radius is R, is turning with an init

Question

A cylindrical turntable whose mass is M and radius is R, is turning with an initial constant angular speed omega 1, . (a) A seagull of mass m, hovering in flight above the outer edge of the turntable, gently lands on it and stays in one place on the rim of the turntable. What is the angular speed of the turntable after the seagull lands? (b) Becoming dizzy, the seagull jumps off (docs 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 seagull speed v and the initial angular speed 1 omega 1. [13]

Explanation / Answer

Moment of Inertia of the table alone is given by MR2/2.

If the bird land on it at the edge then the total moment of inertial changes to (MR2/2+mR2)

As angular momentum is conserved,

(MR2/2).1=(M/2+m).R2.

thus =1.{M/(M+2m)}

As soon as the bird leaves the table the angular momentum about the axis of rotation of the table is conserved.

(MR2/2).1=(MR2/2).2+mR2.v/R

2=1-2mv/MR

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