A $400\mathrm{g}$ particle is moving in circular motion with a radius of $2.3\mathrm{m}$. At one instant in time its speed was $3.4\mathrm{m}/\mathrm{s}$ and it was slowing down at a rate of $2.2\mathrm{m}/{\mathrm{s}}^2$. What was the magnitude of the net force on the particle at this instant?

(II) A solid rubber ball rests on the floor of a railroad car when the car begins moving with acceleration a. Assuming the ball rolls without slipping, what is its acceleration relative to

(b) the ground?

(II) Calculate the moment of inertia of the array of point objects shown in Fig. 10–58 about the y axis, and the x axis. Assume m = 22kg, M = 3.2kg, and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the x axis.

(c) About which axis would it be harder to accelerate this array?

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(II) A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 330 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?

Suppose that piano has a long, thin bar ran through it (totally random), shown below as the vertical red line, so that it is free to rotate about a vertical axis through the bar. You push the piano with a horizontal 100 N (blue arrow), causing it to spin about its vertical axis with 0.3 rad/s² . Your force acts at a distance of 1.1 m from the bar, and is perpendicular to a line connecting it to the bar (green dotted line). What is the piano's moment of inertia about its vertical axis?