Rotational movement. Circular movement. Equation of motion in a circle. Angular velocity. Normal = centripetal acceleration. Period, frequency of circulation (rotation). Relationship between linear and angular speed Calculation of revolutions per minute
Revolutions per minute
Car tachometer (indicator of engine revolutions per minute)
Revolutions per minute(designation rpm, 1 min, min −1, the English designation is also often used rpm) - unit of rotation speed: the number of full revolutions made around a fixed axis. Used to measure the rotation speed of mechanical components.
The unit is also used revolutions per second(symbol r/s or s −1). RPM is converted to RPM by dividing by 60. The reverse conversion is RPM multiplied by 60.
1 rpm = 1/min = 1/(60s) = 1/60 r/s ≈ 0.01667 r/s
Another physical quantity is associated with this concept: angular velocity; in the SI system it is measured in radians per second (rad s −1):
1 rpm = 2π rad min −1 = 2π/60 rad s −1 = 0.1047 rad s −1 ≈ 1/10 rad s −1
Examples
see also
Notes
Wikimedia Foundation. 2010.
See what “Revolutions per minute” is in other dictionaries:
revolutions per minute- Unit of measurement used to characterize centrifugation parameters by rotor rotation speed (along with the g indicator, gravity acceleration). [Arefyev V.A., Lisovenko L.A. English-Russian explanatory dictionary of genetic terms 1995... ... Technical Translator's Guide
Rpm (round per minute) revolutions per minute. A unit of measurement used to characterize centrifugation parameters by rotor rotation speed (along with the g indicator, gravity acceleration). (Source: “English-Russian explanatory dictionary... ... Molecular biology and genetics. Dictionary.
Non-system units rotation speed. Designation rpm 1 rpm = 1 min 116.667 s 1 ... Big Encyclopedic Polytechnic Dictionary
Turns, m. 1. Full circle of rotation, circular turn. Wheel revolution. The shaft makes 20 revolutions per minute. || Moving back and forth, returning to the starting place. Speed up the turnover of wagons. 2. A separate stage, a completed process in a sequential... ... Ushakov's Explanatory Dictionary
- (Revolution) on fleet vessels, in relation to the operation of the main machine, a full rotation (860°) of the propeller shaft rotated by this machine. To have so many revolutions is an order in a machine, requiring that the propeller shaft give a specified number of revolutions per minute ... Marine Dictionary
This term has other meanings, see Verso. Revolution (cycle, circle) is a unit of measurement of angle or phase of oscillation. When measuring angle, the name "revolution" is usually used, and when measuring phase, "cycle". One revolution is equal to... ... Wikipedia
Noun, m., used. compare often Morphology: (no) what? turnover, what? turn around, (I see) what? turnover, what? in turn, about what? about turnover; pl. What? revolutions, (no) what? revolutions, what? revolutions, (I see) what? rpm, what? revs, about what? about revolutions 1... Dmitriev's Explanatory Dictionary
turnover- A; m. see also. negotiable, turnover 1) a) Full circle of rotation; circular turn. Revolution/t of wheel. Number of revolutions per minute. Turn the key two turns... Dictionary of many expressions
A; m. 1. Full circle of rotation; circular turn. O. wheels. Number of revolutions per minute. Turn the key two turns. // Special Turning from one side to the other, reverse. Plowing with formation turnover. // plural: revolutions, ov. Specialist. decomposition ABOUT… … encyclopedic Dictionary
number of circular divisions per minute- 3.1 dial division per minute: The speed of rotation of the stirrer used in this method. Note One complete rotation of the stirrer (360°) is divided into 100 divisions. The turnover rate is characterized by speed... ... Dictionary-reference book of terms of normative and technical documentation
>>Physics: Period and frequency of revolution
Uniform circular motion is characterized by the period and frequency of revolution.
Circulation period- this is the time it takes to complete one revolution.
If, for example, during a time t = 4 s a body, moving in a circle, made n = 2 revolutions, then it is easy to understand that one revolution lasted 2 s. This is the period of circulation. It is designated by the letter T and is determined by the formula:
So, to find the period of revolution, you need to divide the time during which n revolutions are made by the number of revolutions.
Another characteristic of uniform circular motion is the rotation frequency.
Frequency- this is the number of revolutions made in 1 s. If, for example, in a time t = 2 s the body made n = 10 revolutions, then it is easy to understand that in 1 s it managed to make 5 revolutions. This number expresses the frequency of circulation. It is denoted by the Greek letter V(read: nude) and is determined by the formula:
So, To find the rotation frequency, you need to divide the number of revolutions by the time during which they occurred.
The SI unit of revolution frequency is the frequency of revolution at which a body makes one revolution every second. This unit is designated as follows: 1/s or s -1 (read: second minus the first power). This unit used to be called "revolutions per second", but this name is now considered obsolete.
Comparing formulas (6.1) and (6.2), one can notice that period and frequency are mutually inverse quantities. That's why
Formulas (6.1) and (6.3) allow us to find the revolution period T if the number n and the revolution time t or the revolution frequency are known V. However, it can also be found in the case when none of these quantities are known. Instead, it is enough to know the speed of the body V and the radius of the circle along which it moves.
To derive the new formula, let us remember that the period of revolution is the time during which the body makes one revolution, i.e., it travels a path equal to the length of the circle ( l env = 2 P r, where P≈3.14 is the number “pi”, known from the mathematics course). But we know that with uniform motion, time is found by dividing the distance traveled by the speed of movement. Thus,
So, To find the period of revolution of a body, you need to divide the length of the circle along which it moves by the speed of its movement.
??? 1. What is the circulation period? 2. How can you find the period of revolution, knowing the time and number of revolutions? 3. What is the frequency of circulation? 4. How is the unit of frequency designated? 5. How can you find the frequency of circulation, knowing the time and number of revolutions? 6. How are period and frequency of circulation related? 7. How can you find the period of revolution, knowing the radius of the circle and the speed of the body?
Submitted by readers from Internet sites
A collection of physics lesson notes, abstracts on a topic from the school curriculum. Calendar thematic planning. 8th grade physics online, books and textbooks on physics. The student prepares for the lesson.
Lesson content lesson notes supporting frame lesson presentation acceleration methods interactive technologies Practice tasks and exercises self-test workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures, graphics, tables, diagrams, humor, anecdotes, jokes, comics, parables, sayings, crosswords, quotes Add-ons abstracts articles tricks for the curious cribs textbooks basic and additional dictionary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in a textbook, elements of innovation in the lesson, replacing outdated knowledge with new ones Only for teachers perfect lessons calendar plan for the year; methodological recommendations; discussion programs Integrated LessonsSometimes questions from mathematics and physics come up in relation to cars. In particular, one such issue is angular velocity. It relates both to the operation of mechanisms and to cornering. Let’s figure out how to determine this value, how it is measured, and what formulas need to be used here.
How to determine angular velocity: what is this quantity?
From a physical and mathematical point of view, this quantity can be defined as follows: these are data that show how quickly a certain point rotates around the center of the circle along which it moves.
WATCH THE VIDEO
This seemingly purely theoretical value has considerable practical significance when operating a car. Here are just a few examples:
- It is necessary to correctly correlate the movements with which the wheels rotate when turning. The angular speed of a car wheel moving along the inner part of the trajectory should be less than that of the outer one.
- You need to calculate how fast the crankshaft rotates in the car.
- Finally, the car itself, when going through a turn, also has a certain value of motion parameters - and in practice, the stability of the car on the highway and the likelihood of capsizing depend on them.
Formula for the time it takes for a point to rotate around a circle of a given radius
In order to calculate angular velocity, the following formula is used:
ω = ∆φ /∆t
- ω (read “omega”) is the actual calculated value.
- ∆φ (read “delta phi”) – rotation angle, the difference between the angular position of a point at the first and last moment of measurement.
- ∆t
(read “delta te”) – the time during which this very shift occurred. More precisely, since “delta”, it means the difference between the time values at the moment when the measurement was started and when it was completed.
The above formula for angular velocity applies only in general cases. Where we are talking about uniformly rotating objects or the relationship between the movement of a point on the surface of a part, the radius and time of rotation, it is necessary to use other relationships and methods. In particular, a rotation frequency formula will be needed here.
Angular velocity is measured in a variety of units. In theory, rad/s (radians per second) or degrees per second are often used. However, this value means little in practice and can only be used in design work. In practice, it is measured more in revolutions per second (or minute, if we are talking about slow processes). In this regard, it is close to the rotational speed.
Rotation angle and period of revolution
Much more commonly used than rotation angle is rotation rate, which measures how many rotations an object makes in a given period of time. The fact is that the radian used for calculations is the angle in a circle when the length of the arc is equal to the radius. Accordingly, there are 2 π radians in a whole circle. The number π is irrational, and it cannot be reduced to either a decimal or a simple fraction. Therefore, if uniform rotation occurs, it is easier to count it in frequency. It is measured in rpm - revolutions per minute.
If the matter concerns not a long period of time, but only the period during which one revolution occurs, then the concept of circulation period is used here. It shows how quickly one circular movement is made. The unit of measurement here will be the second.
The relationship between angular velocity and rotation frequency or rotation period is shown by the following formula:
ω = 2 π / T = 2 π *f,
- ω – angular velocity in rad/s;
- T – circulation period;
- f – rotation frequency.
You can get any of these three quantities from another using the rule of proportions, without forgetting to convert the dimensions into one format (in minutes or seconds)
What is the angular velocity in specific cases?
Let's give an example of a calculation based on the above formulas. Let's say we have a car. When driving at 100 km/h, its wheel, as practice shows, makes an average of 600 revolutions per minute (f = 600 rpm). Let's calculate the angular velocity.
Since it is impossible to accurately express π in decimal fractions, the result will be approximately 62.83 rad/s.
Relationship between angular and linear speeds
In practice, it is often necessary to check not only the speed with which the angular position of a rotating point changes, but also its speed in relation to linear motion. In the example above, calculations were made for a wheel - but the wheel moves along the road and either rotates under the influence of the speed of the car, or itself provides it with this speed. This means that each point on the surface of the wheel, in addition to the angular one, will also have a linear speed.
The easiest way to calculate it is through the radius. Since the speed depends on time (which will be the period of revolution) and the distance traveled (which will be the circumference), then, taking into account the above formulas, the angular and linear speed will be related as follows:
- V – linear speed;
- R – radius.
From the formula it is obvious that the larger the radius, the higher the value of this speed. In relation to the wheel, the point on the outer surface of the tread will move with the highest speed (R is maximum), but exactly in the center of the hub the linear speed will be zero.
Acceleration, moment and their connection with mass
In addition to the above values, there are several other issues associated with rotation. Considering how many rotating parts of different weights there are in a car, their practical importance cannot be ignored.
Even rotation is important. But there is not a single part that rotates evenly all the time. The number of revolutions of any rotating component, from the crankshaft to the wheel, always eventually rises and then falls. And the value that shows how much the revolutions have increased is called angular acceleration. Since it is a derivative of angular velocity, it is measured in radians per second squared (like linear acceleration - in meters per second squared).
Another aspect is associated with movement and its change in time - angular momentum. If up to this point we could only consider purely mathematical features of movement, then here we need to take into account the fact that each part has a mass that is distributed around its axis. It is determined by the ratio of the initial position of the point, taking into account the direction of movement - and momentum, that is, the product of mass and speed. Knowing the moment of impulse arising during rotation, it is possible to determine what load will fall on each part when it interacts with another
Hinge as an example of impulse transmission
A typical example of how all the above data is applied is the constant velocity joint (CV joint). This part is used primarily on front-wheel drive cars, where it is important not only to ensure different rates of rotation of the wheels when turning, but also to control them and transfer the impulse from the engine to them.
WATCH THE VIDEO
The design of this unit is precisely intended to:
- compare with each other how quickly the wheels rotate;
- ensure rotation at the moment of turning;
- guarantee the independence of the rear suspension.
As a result, all the formulas given above are taken into account in the operation of the CV joint.
