What is an angular velocity and how to deal with it
In terms of physics, when talking of the angular velocity, one should mean a phenomenon also called as a rotational velocity, which are both scientific expressions of certain quantity of rotation. This is the rotation that a particular spinning object can undergo within a certain unit of time. In other words, it is a vector quantity, which usually consists of that or another speed component and of a couple of identified senses (which can also be directions). To understand the definition and meaning of the angular velocity is not really easy, it requires having appropriate background in physics. The term angular velocity is used mostly in physic, but you can meet it also within your studying of other disciplines, such as chemistry or mathematics. In addition, you can also face the term of angular velocity if you are going to deal with mechanics or engineering. As we have already said, understanding of the angular velocity is difficult. However, in this article, we are trying to explain what is angular velocity in as understandable way as possible. Keep reading attentively to learn more.
An angular velocity, which is supposed to express the quantity of rotation of that or another spinning object within certain period of time, is a specific vector, which identifies the quantity which consists of a certain component of speed and of two particular directions.
Apart from knowing what is an angular velocity, you should also know what is the length, which is sometimes also called the magnitude of the phenomenon that we are discussing. Generally speaking, when talking of the length of an angular velocity, one should mean an expression that is directly proportional to the speed of the angle. The magnitude of the angular velocity can be measured by means of several approaches. One of these approaches is quite in the same units as angular speed. You must have heard already about revolutions per minute, degrees per minute or degrees per second or revolution per second and so on. As a matter of fact, the direction of the angular velocity is usually perpendicular to the ground (as a rule, it is a plane) where the rotation is located. In case if the rotation is seen moving from left to the right, then it means that the vector of the angular velocity directs far away from the one who is observing it. On the other hand, in case if the rotation is seen moving tin the opposite direction, from right to the left, it means that the angular velocity directs right toward the one who is observing it at the moment. Therefore, there can be two kinds of directions of the angular velocity, which is important to take into consideration when solving an assignment on physics.
Have a vivid image of the angular velocity
Take into consideration a car driving right forward along a highway. This will help you create an image of what we are now discussing and understand the discussed issue much better. You can see how a car is moving while all four tires are representing its vectors of the angular velocity. As you can see, all the vectors are directed to the left along the lines consisting of the wheel axles.
There would be several options of what can happen next. In the first one, in case if the speed of the car increases, all the four vectors are going to get longer. In case if the speed of the car decreases, all the four vectors are bound to get shorter. At the same time, in case if the car stops, it will lead to the situation where the vectors are just zero. However, if you imagine a situation where a car is put into reverse, you will see that in this case all the four vectors will do the same, they will reverse their directions and will remain directed toward the right along the defined lines consisting of the wheel axles.
Dealing with calculating the angular acceleration
Apart form the fact that you need to be aware of the definition and the common meaning of the term angular velocity, it is also very important to know and understand to what situations you can apply your knowledge and how this knowledge can appear to be useful to you. In addition to the term angular velocity, you have probably faced such term as angular acceleration. This is a term which is usually expressed through the symbol α, it serves to provide a measurement of that or another rate of change of the angular velocity considering respect to certain period of time. In order to understand this issue deeply, it is important to be aware of the basics considering the angular distance, as well as considering the angular velocity. The last one plays a very significant role in the formula describing how to find the angular acceleration. At the same time, the angular distance is an expression describing the measure of change in rotation within a certain period of time. In any case, if you have an assignment requiring you to calculate the angular acceleration, keep reading further carefully, because below we provided steps that you will have to undertake in order to cope with this task.
- First of all, you will have to check your rotating body. Before you actually proceed to calculating, you need to ensure that the body provided in the assignment is moving in a circle that you can call perfect around certain axis. Visualizing may be helpful in this deal, so try to imagine how you tie an end of a certain rope to a stone, while grabbing the other end and swirling it. Thus, you will get the vertical line which will be passing through your hand. This is going to be the axis of rotation, while the stone itself is going to be the rotating body.
- The next step is making sure that you know and understand the angular position. When talking of an angular position, one should mean a specific body which is rotating around the same axis. The angular position, depending on the situation, can be rather positive or negative. The angles are positive in case if they can be measured in a direction from left to the right. Quite the opposite, the angles are considered negative in case if they can be measured in a direction from right to the left.
- Keep in mind that the angular position is in that or another way an angular velocity in a certain period of time.
- After that, you will have to identify the position of the angle. In order to measure the angular velocity at a certain period of time, it is essential to be aware of the position of the given body.
- Now that you have found out the position of the given body, you can proceed to measuring the angular velocity. As we have already said, you are going to deal with a derivative with respect to certain period of time. Here, the derivative is going to be the rate of particular position change within a very little amount of time.
- Once you have found the angular velocity, it is time for determining the angular acceleration. This will give you information considering the rate of the change of the angular velocity over certain period of time. In terms of mathematics, the angular acceleration that you have found will determine the derivative of the velocity of the angle.
How to manage calculating the radial velocity
If your assignment asks you to find the radial velocity, it means that you will have to calculate the speed, which is peculiar to the rotating object. This is quite a common assignment. In order to learn how to cope with it, read the following guidelines.
- At first, you need to identify the value of the linear velocity of the given object. At the same time, you will also need to find out the radius of the object. These values that you will find have to match each other in units.
- After that, you will need to measure the circumference. Keep in mind that this kind of value should be expressed in meters or they also can be expressed in feet. It depends in what your assignment requires.
- The next step will be calculating of the revolutions per second. You can deal with it by dividing the number identifying the velocity by the number identifying the circumference.
- Now it is time to convert the revolutions per second to radians. Here, you will have to deal with arc measure. Remember that radians are always an arc measure. By this, we mean that one radian expresses the length of one radius of any circle. This is going to be your final step.
Check out tips for calculating the radial velocity
Remember that all the units have to be similar. Whatever kind of units you are working with, make sure that you keep all of them similar. The most reliable method to keep your answer correct is saving values in the calculator that you use when completing your assignment. Thus, you will always have an opportunity to return to previous steps in order to improve your mistake, if such exists.
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