A 450.0?g bird is flying horizontally at 2.00m/s , not paying much attention, wh

Question

A 450.0?g bird is flying horizontally at 2.00m/s , not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0cm below the top (the figure (Figure 1) ). The bar is uniform, 0.760m long, has a mass of 1.40kg , and is hinged at its base. The collision stuns the bird so that it just drops to the ground afterward (but soon recovers to fly happily away).

What is the angular velocity of the bar just after it is hit by the bird?

A 450.0-g bird is flying horizontally at 2.00m/s , not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0cm below the top (the figure (Figure 1) ). The bar is uniform, 0.760m long, has a mass of 1.40kg , and is hinged at its base. The collision stuns the bird so that it just drops to the ground afterward (but soon recovers to fly happily away). What is the angular velocity of the bar just after it is hit by the bird? What is the angular velocity of the bar just as it reaches the ground?

Explanation / Answer

Here ,

moment of inertia of gate I = ml^2/3

I = 1.40 * 0.76^2 /3

I = 0.27 Kg.m^2

Using conseravtion of angular momentum ,

I*wi - mvr = 0

0.27 * wi = 0.450 * 2 * (0.76 - 0.25)

wi = 1.7 rad/s

the angular velocity of rod just after collision is 1.7 rad/s

B)

Using conservation of energy ,

0.5 * 0.27 * wf^2 = 0.5 * 0.27 * 1.7^2 + 0.76 * 9.8 * 1.4/2

solving for wf

wf = 6.44 rad/s

the angular velocity just before hitting floor is 6.44 rad/s

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