Why are vectors important in physics

Momentum vectors are useful when you want to predict what will happen when two objects come into contact. Recall from the video that vectors can be added together by joining them to make a shape called a parallelogram and finding the diagonal of that parallelogram.

The diagonal is the sum of the two vectors that form the sides of the parallelogram. Let's say that a rolling billiard ball is moving toward a glancing collision with a stationary billiard ball.

On impact, the moving ball transfers some of its momentum to the stationary ball, and both roll away from the collision in different directions. Following the impact, both balls have velocity and hence momentum. In fact, the sum of the momentum vectors of the two balls after the collision is equal to the first ball's momentum vector before the collision, ignoring small losses due to friction as well as sound and heat energy produced during the impact.

So, with an understanding of vectors, billiards players can predict where both balls will go following a collision, allowing them to sink more target balls while keeping the cue ball safely on the table. Already a subscriber? Sign in. Thanks for reading Scientific American. Create your free account or Sign in to continue.

If you try to add together vector quantities without taking into account their direction you'll get results that are incorrect. Some of the key vector quantities in physics: force, displacement, velocity, and acceleration. An example of the importance of vector addition could be the following: Two cars are involved in a collision. At the time of the collision car A was travelling at 40 mph, car B was travelling at 60 mph.

Until I tell you in which directions the cars were travelling you don't know how serious the collision was. The cars could have been travelling in the same direction, in which case car B crashed into the back of car A, and the relative velocity between them was 20 mph.

Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of mph! Why are vectors important in physics? To test your understanding of this distinction, consider the following quantities listed below. Categorize each quantity as being either a vector or a scalar.

Click the button to see the answer. This is a scalar ; there is no direction listed for it. This is a vector ; a direction is listed for it. Physics Tutorial. My Cart Subscription Selection. Student Extras.