*Reference:** Beginning Physics I*

**CHAPTER 3: MOTION IN A PLANE**

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**KEY WORD LIST**

**Vector, Scalar, Component of A Vector, Displacement In A Plane, Velocity In A Plane, Acceleration In A Plane, Component Method For Motion, Trajectory Equation, Uniform Circular Motion, Centripetal Acceleration, Periodic Motion, Period, Relative Motion**

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## GLOSSARY

For details on the following concepts, please consult **CHAPTER 3**.

**VECTOR**

Any physical quantity that is described by a magnitude and a direction is called a **vector** quantity. A vector is defined geometrically by means of an arrow. The length of the arrow is the magnitude of the vector, and the direction of the arrow is the direction of the vector. The value of the vector does not depend on where it is located on the graph, *only* on its magnitude and direction. You may study this chapter for ** Rules of vector algebra**.

**SCALAR**

These are ordinary algebraic quantities having only magnitude. They are representable by position on a scale or line.

**COMPONENT OF A VECTOR**

The component of vector in a given direction equals plus or minus the magnitude of the vector times the cosine of the acute angle with that direction. The correct sign is then chosen by inspection. A knowledge of the two components of a two-dimensional vector uniquely determines the magnitude and direction of the vector.

**DISPLACEMENT IN A PLANE**

The displacement in a plane ** r** has a horizontal component

*r*and a vertical component

_{x}*r*.

_{y}**VELOCITY IN A PLANE**

The instantaneous velocity in a plane ** v** has a horizontal component

*v*and a vertical component

_{x}*v*.

_{y}**ACCELERATION IN A PLANE**

The instantaneous acceleration in a plane ** a** has a horizontal component

*a*and a vertical component

_{x}*a*.

_{y}**COMPONENT METHOD FOR MOTION**

We see that the motion of a particle can be analyzed by studying the motion of particle’s shadows on the different axes of the coordinate system, each of which is a one-dimensional motion. If we know everything about the shadow motions along the axes, we can reconstruct the full two- or three-dimensional motion.

**TRAJECTORY EQUATION**

The trajectory equation is the equation for the path of the projectile in the xy plane, that is, to obtain an equation for y in terms of x.

**UNIFORM CIRCULAR MOTION**

This is the case of an object moving with constant speed v around a circular path of radius r. It has the peculiar property that while the magnitude of the velocity is just the constant speed v, the direction of the velocity is continually changing.

**CENTRIPETAL ACCELERATION**

The centripetal acceleration is the acceleration of a particle in uniform circular motion. It is strictly due to the change in direction of the velocity **v**. It points toward the center of the circular path. Its magnitude is,

Thus, just as for the velocity, the acceleration has constant magnitude but changing direction.

**PERIODIC MOTION**

Periodic motion is the motion that repeats itself over and over. The uniform circular motion is an example of it.

**PERIOD**

A period (*T*)is the time for one repetition of the periodic motion. For uniform circular motion, *v* equals the distance traveled in one revolution divided by the time to complete the revolution, or *v = 2πr/T.*

**RELATIVE MOTION**

A velocity has meaning only when it is measured relative to something that is assumed to be at rest.

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