Question

A circular bird feeder of radius R and moment of inertia I is suspended at its center by a thin wire. (The feeder is oriented in a horizontal plane.) A bird of mass mB lands on the rim of the feeder, coming in with a velocity tangent to the rim. After the bird lands, the angular velocity of the feeder is measured to be omega. Find the incoming speed of the bird in terms of the moment of inertia and radius of the feeder, the mass of the bird, and the angular velocity of the feeder after the landing. In addition, give a numerical result assuming that the radius of the feeder is 5.0 cm, the moment of inertia of the feeder is 1.0 x 10^-4 kg·m^2, the mass of the bird is 10 g, and the final angular velocity of the feeder (and bird) is 2.0 rad/s.

Answer 1

Step-by-step explanation:

Let velocity of coming bird initially be v .

angular momentum of the bird about center of circular bird feeder

= mB x v x R

Total moment of inertia of bird and feeder = I + mB x R²

Applying conservation of momentum

mB v R = ( I + mB x R²) ω

ω = mB v R / ( I + mB x R²)

v = ( I + mB x R²)ω / mB R

Putting the numerical values

v = (.0001 + .01 x .05²) x 2 / (.01 x .05 )

= .5 m / s .