In lesson one we learned the difference between speed and velocity. This difference was that velocity requires that a direction be specified. Any quantity that requires both magnitude (speed) and direction is called a vector quantity. Any quantity that only requires magnitude is called a scalar quantity. So velocity is a vector quantity and speed is a scalar quantity. We represent a vector quantity with an arrow. We represent a scalar quantity with a point.

You are able to add vectors. The sum of two vectors is called the resultant. If you have two vectors moving in parallel directions, they can be added with straight addition. For example, a plane moving at 100 km/hr east with a tailwind of 50 km/hr east is moving at a velocity of 150 km/hr east. If the tailwind becomes a headwind, then the plane is moving at 50 km/hr east.

Adding vectors that are not parallel is a little bit more difficult. Here's how you do it. Draw in the first vector. At the tip of that vector, draw in the second vector. The resultant is the distance (and direction!) from the beginning of the first vector to the end of the second vector. This sounds a little bit confusing. Let's go through it step by step. Our plane is now going at 50 km/hr to the west with a wind going 50 km/hr to the north.

Mouse Over to View Animation

Since this is a right triangle, we can solve for the magnitude of the new vector with the Pythagorean theorem. We find that the plane is moving at 70.7 km/hr at 45 degrees north west.

A projectile is any object that is projected by some means and continues in motion under the influence of gravity. The path that a projectile follows is called a trajectory. All trajectories are parabolas, and the motion of a projectile can be represented by a horizontal and vertical vector. These are the horizontal component of motion and the vertical component of motion.

The horizontal component of projectile motion never changes. It remains the same during the entire trajectory. If a ball is thrown with a horizontal velocity of 5 km/hr, it will be moving with a horizontal velocity of 5 km/hr until it hits the ground. The vertical component of a projectile is a little bit more complex. Remember from the last lesson that an object in free fall accelerates at 9.8 meters per seconds squared. Well, an projectile accelerates downwards at the same rate. So the vertical component of projectile motion is constantly changing-but at a rate that we know. A consequence of this is that a projectile will fall below the straight line path that it would follow without gravity the same distance a object in free fall would fall in the same time. Whew! Let's look at that.

Now we will visit the special cases of circular motion. To do this we need to clarify some terms that we have been using. When we have used the term "speed" in the past we were talking about linear speed. This is the distance moved per unit of time. When something is moving in a circle, we use the term tangential speed. We can use tangential speed and linear speed interchangeably. Rotational speed is something else. It refers to the number of rotations per unit of time. It is commonly referred to in the units RPM (revolutions per minutes.)

Thinking of these terms, is a horse on the edge of a merry go round moving faster or slower than a horse close to the center of the merry go round? Your answer depends on the type of speed you are talking about. If you want to talk about tangential or linear speed, then the horse on the outside is moving faster than the horse on the inside, because it is covering a greater distance in the same amount of time. If you wish to talk about rotational speed, then the two horses are moving the same speed, because they both make the same number of rotations in the same amount of time. However, rotational speed and tangential speed are related. If the rotational speed is increased, then the tangential speed also increases. This makes sense, because the greater the RPMs, the faster your speed in meters per second.

Mouse Over to View Animation