sg11 - Chapter 11 Study Guide for Motion in a Plane 11.1...

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Chapter 11 Study Guide for Motion in a Plane 11.1 Straight is a relative term Skill 11.1 Understand the theory behind decomposition of motion As we saw in Chapter 7, our choice of reference frame affects measurements of quantities such as position and velocity; a ball may appear to drop straight down in one reference frame and appear to follow a curved path in another reference frame (Look at Figure 11.2). An object’s motion in two dimensions can be broken down into two one-dimensional problems. For example, one might break the two-dimensional problem of a dropping ball following a curved path into one problem involving the object’s vertical motion and one problem involving the object’s horizontal motion. 11.2 Vectors in a plane Skill 11.2 Be able to graphically add and subtract vectors in a plane To specify the position of an object in a two-dimensional space, we need two coordinates: one for the object’s position along the horizontal, or x-axis, and one for the object’s position along the vertical, or y-axis. Two-dimensional vectors can point along any direction in the two-dimensional space; they do not have to point along the x- or y-axis. The rule for graphically adding vectors in two dimensions is exactly the same as the one for adding vectors in one dimension. To obtain the vector sum, simply place the tail of the second vector at the head of the first one (Look at Figure 11.7). The vector sum then points from the tail of the first vector to the tip of the second vector. To subtract a vector b from a vector a , invert the direction of b and add the inverted b to a . Note: Unlike the one-dimensional case, the magnitude of vector sums in two dimensions is not necessarily the sum of the magnitudes of the vectors being added. Skill 11.3 Be able to graphically decompose vectors in a plane into two vector compo- nents Any vector in a plane can be decomposed into two vector components. One common way to do this is to define a rectangular coordinate system, in which the x- and y-axes are perpendicular. The vector then has a component along the x-axis and a component along the y-axis. These are its two vector components. Look at Figure 11.8 to see a vector graphically decomposed into its two vector components. Skill 11.4 Understand how the angle between an object’s acceleration vector and its instantaneous velocity vector relates to the change in direction of its instantaneous velocity vector and its speed In two-dimensional motion, the acceleration vector does not always point along or against the instantaneous velocity vector (as it does in one-dimensional motion). 1
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To figure out how this affects the motion of the object, we have to decompose the acceleration vector into two components: one parallel to the instantaneous velocity and one perpendicular to it.
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