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You have seen that a force acts between two or more charged objects In your experiments with tape, you found that the force depends on distance The closer you brought the charged comb to the tape, the stronger the force was You also found that the more you charged the comb, the stronger the force was How can you vary the quantity of charge in a controlled way This problem was solved in 1785 by French physicist Charles Coulomb The type of apparatus used by Coulomb is shown in Figure 20-10 An insulating rod with small conducting spheres, A and A , at each end was suspended by a thin wire A similar sphere, B, was placed in contact with sphere A When they were touched with a charged object, the charge spread evenly over the two spheres Because they were the same size, they received equal amounts of charge The symbol for charge is q Therefore, the amount of charge on the spheres can be represented by the notation qA and qB Force depends on distance Coulomb found how the force between the two charged spheres depended on the distance First, he carefully measured the amount of force needed to twist the suspending wire through a given angle He then placed equal charges on spheres A and B and varied the distance, r, between them The force moved A, which twisted the suspending wire By measuring the deflection of A, Coulomb could calculate the force of repulsion He showed that the force, F, varied inversely with the square of the distance between the centers of the spheres F

this purpose is a small plastic test tube about four inches long and two-thirds of an inch in diameter; it turned out to be comfortable to use, but it was a challenge to squeeze the logic probe circuit into such a small space To give you a sense of the size of the probe, Figure 6-6 is a photo of the completed project next to a mechanical pencil The parts list for the stripboard version of the logic probe circuit are listed in the Parts Bin, and the stripboard layout is presented in Figure 6-7 We ll discuss the specifics when we actually construct the probe, but there are a couple of points related to the stripboard layout that I want to clarify before we begin First, in the layout, you might have noticed that there are no holes in column AD This is because I included the end of the stripboard (which has no holes in it) in this project because I wanted to be able to round the end of the board to match the curve of the bottom of the test tube, and I preferred not having holes in that area If you look closely at the photo in Figure 6-6, you can see that the end of the board has been rounded

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What if angular velocity is changing For example, if a car were accelerated from 00 m/s to 25 m/s in 15 s, then the angular velocity of the wheels also would change from 00 rad/s to 78 rad/s in the same 15 s The wheels would undergo angular acceleration, which is defined as the change in angular velocity divided by the time required to make the change Angular acceleration, , is represented by the following equation Angular Acceleration of an Object

t Angular acceleration is equal to the change in angular velocity divided by the time required to make that change

Angular acceleration is measured in rad/s2 If the change in angular velocity is positive, then the angular acceleration also is positive Angular acceleration defined in this way is also the average angular acceleration over the time interval t One way to find the instantaneous angular acceleration is to find the slope of a graph of angular velocity as a function of time The linear acceleration of a point at a distance, r, from the axis of an object with angular acceleration, , is given by a r Table 8-1 is a summary of linear and angular relationships

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