Benchmark 1

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A solid  metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures show forces of different magnitudes that are exerted on the bar at different locations. In which case does the bar's angular speed about the axis increase at the fastest rate?

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Tiny drops of oil that have different amounts of electric charge produced by a random process are sprayed into a region between a positively and a negatively charged plate. The charge on each drop is determined by analyzing the effect of the electric force on the drop's motion. Two graphs of the number of drops as a function of the charge on eacd drop, where e is the charge of an electron. Which graph shows the likely results after repeating the experiment many times and why? 

• Graph 1, because it shows peaks with approximately the same amplitude
• Graph 1, because it shows that within experimental error charge only exists in multiples of e
• Graph 2, because it shows a peak value at the charge of an electron
• Graph 2, because it shows a narrower range of measurement error

A stone disk is sliding on a frictionless ice to the west with speed v. As the disk slides by, a child uses a rubber mallet to hit the disk at point X, exerting a force directly toward the center of the disk. The child hits point X every half second for about 10 s, changing the trajectory of the disk but not causing it to rotate. Which of the following most closely approximates the path of the disk while the child is hitting it?

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• F_B = F_A = F_g
• (F_B = F_A) < F_g
• F_B < (F_A = F_g)
• F_g < F_B < F_A

A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it. The outside edge of the disk is moving at a linear speed v, and the clay is moving at a speed of v/2. The clay sticks to the outside edge of the disk. How does the angular momentum of the system after the clay sticks compare to the angular momentum of the system before the clay sticks, and what is an explanation for the comparison?

• It is the same because there is no external torque acting on the system
• It is greater because the rotating mass increases, which increase the rotational intertia
• It is less because the speed of the disk decreases when the clay sticks to it
• It is less because the angular momentum of the clay opposes that of the disk