1) Three small balls of mass 4.4 kg, 1.7 kg, and 3.5 kg are connected by light rods laying along the y-axis. The rod connecting the first and second balls is 4.1 m long and the rod connecting the second and third balls is 2.1 m. The entire system rotates around the x-axis, which is between the first and second balls and a distance 2.8 m from the first ball, at a rotational speed 2.8 s-1
(a)What is the moment of inertia about the x-axis
(b) What is the rotational kinetic energy of the system?
(c) What are the speeds of the three objects? First Object: Second Object: Third Object:
(d) What is the kinetic energy of each of the balls? First Object: Second Object: Third Object:
(e) What is the total kinetic energy of the system?

2) A war wolf is a device used during the middle ages to assault fortifications with large rocks. A simple trebuchet is constructed with a large, stiff 4 m rod (assume it has negligible mass) with a heavy object of mass 64 kg and 19 cm from the axle around which the device pivots and a cup on the far end that holds the rock. The war wolf is loaded when it is in a horizontal position, and the rock is projected horizontally when after it has rotated to a vertical position.
If the rock has a mass of 133 g, how fast (linear speed) does it move when launched?

3) An unmounted tire of wall radius 33.7 cm has a uniform tread thickness of 3 cm and width 19.4 cm. Its side walls have a thickness of 0.76 cm and a width of 15.4 cm. Assume that rubber has a density of 1.25 g/cm3.
Find the moment of inertia of the tire if it turns around its center.

4) A 1.14 m light, rigid rod joins two particles of masses 3.65 kg and 5.26 kg at its ends. What is the moment of inertia of the system around the center of mass of the system?

5) A laden airplane of mass 331250 kg flies at a constant speed of 152m/s directly over a farmer at a constant altitude of 4 km. The plane flies westward (take x̂ to be directly east and to be directly north) towards the peak of a mountain of height 4 km that is 282 km away.
(a)What is the airplane's vector angular momentum relative to the farmer?
(b) What is the airplane's vector angular momentum relative to the mountain peak?

6) A physical pendulum consists of a vertical board of of mass 6.36 kg, length 191 cm, and width 14 cm hanging from a horizontal, frictionless axle. A bullet of mass 146 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle.
(a) If the bullet passed through the board, reducing its speed by a factor of 1/4, what is the minimum speed of the bullet?
(b) If the bullet embedded itself in the board, what is the minimum speed of the bullet?

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