Drawing Physics pdf download

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PDFs have never been collaborative. Now they are. Sum the components of A! Verify your answers with a numerical calculation. Answers to Your Turn problems are given in the back of the book. Subtracting Vectors Next, how do we subtract! Suppose, for example, that we would like to determine the vector D, where!

To find D, we start by rewrit- ing it as follows:! That is, D is the sum of A and -B. That is, multi- plying a vector by minus one reverses its direction. For example,! Thus, to subtract B from A, simply reverse the direction of B and add it to A, as indicated in Figure 3—14 b. B In terms of components, you subtract vectors by simply subtracting the com- ponents. For example, if —B! Find D and u and compare with the vector D shown in Figure 3—14 b.

A Solution D a. In Figure 3—14 b we see that D is shorter than B, which has a magnitude of 4. Vector subtraction! A vector b! Figure 3—15 shows xN and yN on a two-dimensional coordinate system. Since unit vectors have no physical dimensions—like mass, length, or time—they are used to specify direction only.

Multiplying by -3 The unit vectors xN and yN point in the increases the magnitude by a factor of 3 and reverses the direction of the vector. This is also shown in Figure 3— In the case of unit vectors—which have a mag- nitude of 1 and are dimensionless—multiplication by a scalar results in a vector with the same magnitude and!

An equivalent way of representing the vec- tor components of a vector is illustrated in Figure 3—17 b. In this case we see that —3A the vector components are the projection of a vector onto the x and y axes. The sign of the vector components is positive if they point in the positive x or y direction, and negative if they point in the negative x or y direction.

This is how vector com- ponents will generally be shown in later chapters. If the vector is multiplied by a! This method of representing vector components will be used frequently in a b subsequent chapters. Each of these quantities had a direc- tion associated with it, indicated by its sign; positive meant in the positive direction, negative meant in the negative direction. Now we consider these vectors again, this time in two dimensions, where the possibilities for direction r are not so limited.

Position is indicated by a vector from the origin to the location in question. We The position vector r points from the! The x and y vector components of r! Definition: Position Vector, r! Definition: Average Velocity Vector, v av!

It points from! What was the! P1 To help visualize v av, imagine a particle moving in two dimensions along the t1 blue path shown in Figure 3— If the particle is at point P1 at time t1, and at P2 at vav! The average velocity is par-! It makes sense physically that v av is paral-! To put it another way, a particle that starts at P1 at the time t1! By considering smaller and smaller time intervals, as in Figure 3—21, it is pos- The average velocity!

Definition: Instantaneous Velocity Vector, v! In addition, the magnitude of the velocity vector is the speed of the particle. Thus, the instantaneous velocity vector tells you both how fast a particle is moving and in what direction. Solution In the limit of vanish-!

Notice that the Definition: Average Acceleration Vector, a av instantaneous velocity vector points in! Since the change in velocity is defined as! Figure 3— Can an object accelerate if its speed is constant? Absolutely—if its direction changes. At the time t i the velocity is v i; at the time t f the velocity is v f. Calcu- lating the average acceleration, we find a nonzero acceleration:! We shall study circular motion in detail in Chapter 6. Definition: Instantaneous Acceleration Vector, a vi!

Eight seconds later it has rounded a corner vf and is now heading north at What is the magnitude and direction of its average acceleration during those 8. Let the positive x direction be east, and the positive y direction be north. For 3. Students can click on the following links to download ICSE class 10 books pdf.

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