A 530.0?g bird is flying horizontally at 2.50m/s , not paying much attention, wh

Question

A 530.0?g bird is flying horizontally at 2.50m/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, 0.750m long, has a mass of 1.30kg , 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

part A:

apply the law of conservation of angular momentum

as Initial Ang momentum = final Ang momentum

so

Birds Ang momemtun = Bars Ang Momentum

so

mvR = IW

here I = moment of inertia = mL^2/3

I = 1.3 * 0.75 *0.75/3 = 0.24375 Kgm^2

so

W =mvR/I

W =    0.530 * 2.5*(0.75-0.25)/0.243

W = 2.72 rad/s

---------------------------------------
apply the law of conservation of Energy

as Initial KE + intial PE

0.5 IW^2 + mgh

here h = 0.75/2 = 0.375 m

total Intial KE = (0.5* 0.243 * 2.72*2.72) + (1.3 * 9.81 * 0.375)

totol KEi = 5.68 J

Just before Impact,

All KE = 5.68

0.5 IW^2 = 5.68

W^2 = 2* 5.689/(0.243)

W = 6.84 rad/sec

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