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Chapter 3
Kinematics in Two
Dimensions; Vectors
3-1 Vectors and Scalars
A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum A scalar has only a magnitude. Some scalar quantities: mass, time, temperature
3-2 Addition of Vectors – Graphical Methods
For vectors in one dimension, simple addition and subtraction are all that is needed. You do need to be careful about the signs, as the figure indicates.
3-2 Addition of Vectors – Graphical Methods
If the motion is in two dimensions, the situation is somewhat more complicated. Here, the actual travel paths are at right angles to one another; we can find the displacement by using the Pythagorean Theorem.
3-2 Addition of Vectors – Graphical Methods
Adding the vectors in the opposite order gives the same result:
3-2 Addition of Vectors – Graphical Methods
Even if the vectors are not at right angles, they can be added graphically by using the “tail-to-tip” method.
3-3 Subtraction of Vectors, and
Multiplication of a Vector by a Scalar
In order to subtract vectors, we define the negative of a vector, which has the same magnitude but points in the opposite direction. Then we add the negative vector:
3-3 Subtraction of Vectors, and
Multiplication of a Vector by a Scalar
A vector V can be multiplied by a scalar c ; the result is a vector c V that has the same direction but a magnitude cV. If c is negative, the resultant vector points in the opposite direction.
