Review of Vectors vs. Scalars - Online Tutor, Practice Problems & Exam Prep

In physics, measurements can be classified as scalars or vectors. Scalars have only magnitude, such as temperature (e.g., 60 degrees Fahrenheit), while vectors include both magnitude and direction, like force (e.g., 100 Newtons North). Distance is a scalar (e.g., 10 meters), whereas displacement is a vector (e.g., 10 meters east). Similarly, speed is a scalar (e.g., 80 miles per hour), while velocity is a vector (e.g., 80 miles per hour west). Understanding these distinctions is crucial for analyzing motion and forces effectively.

Review of Vectors vs. Scalars

Hey, folks. So we're going to be working a lot with vectors in later videos. In this video, I just wanted to quickly review the difference between vectors and scalars just in case it's been some time since you've seen this stuff. Let's check it out. Remember that the basic idea is that when you take measurements in physics, you always get the size, the magnitude of the measurement, or how much. It's basically just the number that you get when you're measuring something. And remember that some measurements also have direction. And measurements with direction are called vectors. That's magnitude and direction. Whereas numbers without direction, so just the number only, are called scalars. We saw a bunch of examples of this. Let's check it out. For instance, if you were to take a thermometer outside and you measure at 60 degrees Fahrenheit, you're measuring temperature. Well, that's the magnitude, but it doesn't make sense to ask which direction those 60 degrees go. You don't have a direction. And so, therefore, this is a scalar.

Now, let's say you were to push a box somewhere and you're pushing with 100 Newtons North. So that's 100 Newtons, which means that you have the magnitude, but you also have the direction. You're pushing in the north direction. So, that means that this is both, and this is a vector, so force is a vector. Then we saw some specific examples that dealt with how far you're moving or how far you're traveling. We saw distance versus displacement. The basic difference is that if you were to tell somebody I walked for 10 meters, that 10 meters is the magnitude, but you don't know which direction you’re going in. No direction, so, therefore, this is a scalar. But then if you tell your friend I walked 10 meters east, well, now you have both. Now you're talking about the magnitude and the direction and, therefore, this is a vector.

And then, we also saw two examples of how fast you're moving, and this was speed and velocity, and they were kind of related to distance and displacement. If you tell your friend I'm driving 80 miles per hour, that doesn't tell us which direction. We just have magnitude only, without the direction. So it's a scalar. But then if you say, well, I drove 80 miles per hour in the west direction. So now you have both magnitude and direction and, therefore, it's a vector. Alright, guys. That's the basic difference between vectors and scalars. That's it for this one.

Here’s what students ask on this topic:

What is the difference between a vector and a scalar in physics?

In physics, a scalar is a quantity that has only magnitude, such as temperature or distance. For example, 60 degrees Fahrenheit or 10 meters are scalars because they do not include any directional information. On the other hand, a vector is a quantity that has both magnitude and direction. Examples include force and displacement. For instance, 100 Newtons North or 10 meters East are vectors because they specify both how much and in which direction. Understanding these distinctions is crucial for analyzing motion and forces effectively.

Is speed a scalar or a vector quantity?

Speed is a scalar quantity. It represents how fast an object is moving but does not provide any information about the direction of motion. For example, if you say a car is moving at 80 miles per hour, you are only describing the magnitude of its motion. In contrast, velocity is a vector quantity because it includes both the speed and the direction of motion, such as 80 miles per hour west.

Why is force considered a vector quantity?

Force is considered a vector quantity because it has both magnitude and direction. For example, if you push a box with a force of 100 Newtons to the north, you are specifying not only how strong the push is (magnitude) but also the direction in which the force is applied. This directional component is essential for accurately describing and analyzing the effects of forces in physics.

How do distance and displacement differ in terms of vectors and scalars?

Distance is a scalar quantity that measures how much ground an object has covered during its motion, without considering the direction. For example, if you walk 10 meters, the distance is simply 10 meters. Displacement, on the other hand, is a vector quantity that measures the change in position of an object and includes both magnitude and direction. For instance, if you walk 10 meters east, your displacement is 10 meters east. This distinction is important for understanding motion in physics.

Can you give an example of a scalar and a vector quantity in everyday life?

Sure! An example of a scalar quantity in everyday life is temperature. For instance, saying it is 70 degrees Fahrenheit outside provides a magnitude but no direction. An example of a vector quantity is wind velocity. If you say the wind is blowing at 15 miles per hour to the north, you are providing both the speed (magnitude) and the direction, making it a vector quantity.