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Unformatted text preview: 67. (a) If we consider a short time interval from just before the wad hits to just after it hits and sticks, we may use the principle of conservation of angular momentum. The initial angular momentum is the angular momentum of the falling putty wad. The wad initially moves along a line that is d /2 distant from the axis of rotation, where d = 0.500 m is the length of the rod. The angular momentum of the wad is mvd /2 where m = 0.0500 kg and v = 3.00 m/s are the mass and initial speed of the wad. After the wad sticks, the rod has angular velocity and angular momentum I , where I is the rotational inertia of the system consisting of the rod with the two balls and the wad at its end. Conservation of angular momentum yields mvd /2 = I where I = (2 M + m )( d /2) 2 and M = 2.00 kg is the mass of each of the balls. We solve mvd M m d 2 2 2 2 = + b gb g for the angular speed: ( ) ( ) ( ) ( ) ( ) ( ) 2 0.0500 kg 3.00 m/s 2 0.148 rad s....
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