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Initial value

Converted value

radians per second radians per day radians per hour radians per minute degrees per day degrees per hour degrees per minute degrees per second revolutions per day revolutions per hour revolutions per minute revolutions per second revolutions per year revolutions per month revolutions per week degrees per year degrees per month degrees per week radians per year radians per month radians per week

More about angular velocity

General information

Angular velocity is vector quantity, which determines the speed of rotation of the body relative to the axis of rotation. This vector is directed perpendicular to the plane of rotation and is determined using the gimlet rule. Angular velocity is measured as the ratio between the angle through which a body has moved, that is, the angular displacement, and the time spent doing so. In the SI system angular acceleration measured in radians per second.

Angular velocity in sports

Angular velocity is often used in sports. For example, athletes decrease or increase the angular velocity of a golf club, bat, or racket to improve performance. Angular velocity is related to linear velocity such that of all the points on a segment rotating about a point on that segment, that is, about the center of rotation, the point furthest from that center moves at the highest linear speed. So, for example, if a golf club is spinning, the end of that club furthest from the center of rotation moves at the highest linear speed. At the same time, all points on this segment move with the same angular velocity. Therefore, by lengthening the club, bat, or racket, the athlete also increases the linear speed, and accordingly the speed of impact transmitted to the ball, so that it can fly a greater distance. Shortening the racket or club, even gripping it lower than usual, on the contrary, slows down the speed of the strike.

Tall people with long limbs have an advantage in terms of linear speed. That is, by moving their legs at the same angular speed, they move their feet at a higher linear speed. The same thing happens with their hands. This advantage may be one of the reasons why primitive societies men hunted more often than women. It is likely that taller humans also benefited in the evolutionary process because of this. Long limbs helped not only in running, but also during hunting - Long hands threw spears and stones with greater linear speed. On the other hand, long arms and legs can be an inconvenience. Long limbs have more weight and additional energy is needed to move them. In addition, when a person runs fast, long legs move faster, which means that when they collide with an obstacle, the impact will be stronger than for people with short legs who move at the same linear speed.

Gymnastics, figure skating and diving also use angular velocity. If an athlete knows the angular velocity, then it is easy to calculate the number of flips and other acrobatic tricks during a jump. During somersaults, athletes typically press their legs and arms as close to their body as possible to reduce inertia and increase acceleration, and therefore angular velocity. On the other hand, during a dive or landing, judges look at how smoothly the athlete lands. At high speeds, it is difficult to regulate the direction of flight, so athletes deliberately slow down the angular velocity by slightly extending their arms and legs away from the body.

Athletes who throw discus or hammer throw also control linear speed using angular speed. If you just throw a hammer without rotating it in a circle for a long time steel wire, increasing the linear speed, the throw will not be so strong, so the hammer is first spun. Olympic athletes rotate on their axis three to four times to increase their angular velocity to the maximum possible.

Angular velocity and data storage on optical media

When data is written to optical media such as compact discs (CDs), the drive also uses angular and linear speeds to measure the speed at which the data is written and read. There are several ways to record data, which use variable or constant linear or angular velocity. So, for example, the mode constant linear speed(in English - Constant Linear Velocity or CVL) is one of the main methods of recording discs, in which data is written at the same speed over the entire surface of the disc. While recording in zonal constant linear speed(in English - Zone Constant Linear Velocity or ZCLV) a constant speed is maintained during recording on a certain part, that is, a zone of the disk. In this case, the disc spins slower when recording on the outer zones. Mode partially constant angular velocity(Partial Constant Angular Velocity or PCAV) allows you to record with a gradual increase in angular velocity until it reaches a certain threshold. After this, the angular velocity becomes constant. The last recording mode is constant angular velocity(Constant Angular Velocity or CAV). In this mode, the same angular velocity is maintained over the entire surface of the disc during recording. In this case, the linear speed increases as the recording head moves further and further towards the edge of the disk. This mode is also used when recording records and computer hard drives.

Angular velocity in space

At a distance of 35,786 kilometers (22,236 miles) from Earth is the orbit in which the satellites orbit. This is a special orbit because bodies rotating in it in the same direction as the Earth travel the entire orbit in about the same time that it takes the Earth to complete a circle on its axis. This is a little less than 24 hours, that is, one sidereal day. Since the angular velocity of rotation of bodies in this orbit is equal to the angular velocity of rotation of the Earth, it seems to observers from the Earth that these bodies are not moving. This orbit is called geostationary.

This orbit is typically placed by satellites that monitor changes in the weather (meteorological satellites), satellites that monitor changes in the oceans, and communications satellites that provide television and radio broadcasting, telephone communications, and satellite Internet. Geostationary orbit is often used for satellites because antennas, once pointed at a satellite, do not need to be pointed a second time. On the other hand, their use is associated with such inconveniences as the need to have a direct field of view between the antenna and the satellite. In addition, the geostationary orbit is far from Earth and transmitting the signal requires the use of more powerful transmitters than those used for transmission from lower orbits. The signal arrives with a delay of approximately 0.25 seconds, which is noticeable to users. For example, during news broadcasts, correspondents in remote areas usually communicate with the studio via satellite; it is noticeable that when the TV presenter asks them a question, they answer with a delay. Despite this, satellites in geostationary orbit are widely used. For example, until recently, communication between continents was carried out mainly using satellites. It has now been largely replaced by intercontinental cables laid across ocean floor; however, satellite communications are still used in remote areas. In the last twenty years, communications satellites have also provided Internet access, especially in remote locations where there is no terrestrial communications infrastructure.

The service life of a satellite is mainly determined by the amount of fuel on board required for periodic orbital corrections. The amount of fuel in satellites is limited, so when it runs out, the satellites are taken out of service. Most often, they are transferred to a burial orbit, that is, an orbit much higher than geostationary. This is an expensive process; however, leaving unnecessary satellites in geostationary orbit risks the possibility of collisions with other satellites. Space in geostationary orbit is limited, so old satellites left in orbit will take up space that could be used by a new satellite. Because of this, many countries have regulations that require satellite owners to sign an agreement that the satellite will be placed in a disposal orbit at the end of its life.

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The productivity and cleanliness of wood processing on machines largely depend on the cutting speed. In machines with rotating cutters, the cutting speed depends on the number of revolutions of the working shaft per minute and the diameter of the circle along which the cutters rotate.

With direct transmission of motion, the number of revolutions of the working shaft is equal to the number of revolutions of the electric motor shaft. This number is indicated in the brand of the electric motor.

The number of revolutions of the working shaft with a belt drive is read using the formula

- "dv-di About,

P d2 "

Where prv- number of revolutions of the working shaft; Pdv - engine speed; d is the diameter of the drive pulley; ■ D2 - diameter of the driven pulley.

Using the same formula, the number of revolutions of the working shaft during a gear drive is determined; Instead of the diameters of the pulleys, the number of teeth of the corresponding gears is taken.

You can also determine the speed of the drive shaft by multiplying the speed of the electric motor by the gear ratio.

Gear ratio called a number showing how many times the diameter of the drive pulley larger diameter driven pulley.

To determine the gear ratio, divide the number of teeth on the drive gear by the number of teeth on the driven gear.

Cutting speed when working with a straight forward movement of the cutter, it is defined as the speed of the cutter in meters per second ( M! sec). At rotational movement cutter, the cutting speed will be the speed of movement of the cutting edge of the cutter but the circle of rotation, 42

For one revolution of the working shaft with a cutter attached to it, the cutting edge of the cutter will travel a path equal to the length of the circle Her rotation, T. e. 2lg, or Nd. per minute cutting edge Det path equal to the circumference of rotation Nd, multiplied by the number of revolutions of the working shaft P,T. e. I Dn. But cutting speed is usually denoted in meters per second. Hence,

% Dn , V m sec,

Where V- cutting speed in m/sec;

L - constant number 3.14;

D- diameter of the cutting edge rotation circle;

P - number of revolutions of the working shaft.

Example. In a circular saw, saw blade diameter d=400 Mm, number about Rotov n=2000 rpm. It is necessary to determine the rubber speed.

Putting numerical notations in the formula, we find:

%dn , 3.14-0.4-2000 314-1-2 ..l, l „. , !>=----------ms- -! = =41.9"40 msec.

Diameter D is always given in millimeters, but in the formula the numerical designation is taken in fractions of a meter (400 mm = 0,4m). This is done because cutting speed is indicated in meters per second. If you take D in millimeters, then the result of solving the formula would be the number 41,866, which would have to be divided by 1000.

To simplify calculations and thereby prevent possible mistakes, a divisor of 1000 is introduced into the formula, expressing D in millimeters

V=-------------- m sec.

This formula in Lately displaces the first one.

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RPM is a measure of how fast an object rotates. Information about the rotational speed of an object helps determine wind speed, gear ratio, engine power, as well as the speed of departure and depth of travel of the bullet. There are several ways to calculate rotation speed, depending on the purpose for which the obtained value will be used. We will look at the simplest of them.

Steps

Counting rotation speed by visual observation

Select a part of the rotating object that is easy to follow. This method works best for items with long levers or handles. An example is an anemometer (a device for measuring wind speed) or a wind turbine. Select a handle or blade and focus on it.

• You can highlight the blade or handle you need, for example, by tying a colored thread to it or applying a strip of paint.

1. Take a chronometer. You will need to time it. A stopwatch or chronometer on a smartphone or tablet will do this perfectly.

   Start the stopwatch.

   Stop counting after 1 minute. This way you will find out the rotation frequency - the number of revolutions of the object per minute.

Gear ratio

Count the number of teeth on the drive wheel. A drive gear is a gear that is connected to a motor or other power source through an axle. The rotation speed of the leading gearbox is usually known.

• In order to this example we will assume that the gearbox has 80 teeth and a rotation speed of 100 rpm.

1. Count the number of teeth on the driven wheel. The driven gearbox is a gear whose teeth mesh with the teeth of the driving gearbox. The teeth of the driving gear push the teeth of the driven gear, which leads to rotation of the entire driven gear. This is exactly the gear whose rotation speed we will calculate.

   • For the purposes of this example, we will take two driven gears of different sizes, one of which is smaller than the drive gear, and the second is larger.
   • The smaller driven gear has fewer teeth compared to the drive gear. The number of teeth of the smaller gear is 20.
   • The larger driven gear has more teeth compared to the drive gear. The number of teeth of the larger gear is 160.

2. Find the ratio of the drive and driven gears. To find out the ratio of two gears, you need to divide the number of teeth on one gear by the number of teeth on the other. Although the right way will divide the number of teeth of the drive gear by the number of teeth of the driven gear or vice versa, we divide large quantity for less.

   • For the smaller driven gear, we divide the number of drive gear teeth (80) by 20 and get 80 / 20 = 4.
   • For the larger driven gear, we divide the number of its teeth (160) by the number of teeth of the drive gear (80) and get 160 / 80 = 2.

3. Driven gear rotation speed. The calculation method will depend on the size of the driven gear relative to the driving gear.

Calculating the rotation speed of a moving bullet

Determine the initial speed of the bullet. Initial or muzzle velocity is the speed at which a bullet passes through a gun barrel at the moment it is fired. This quantity is usually measured in meters per second (m/s).

• For the purposes of this example we will assume that starting speed is 610 m/s.

1. Determine the rotation speed in the barrel. Inside a gun barrel there are helical grooves or riflings that give the bullet spin. The rotation helps stabilize the bullet's flight after leaving the barrel and on its way to the target. The rotation speed is indicated as the ratio of 1 revolution to the length in millimeters.

In mechanical engineering, gear ratio is a measure of the ratio of the rotational speed of two or more meshed gears. Typically, when we are dealing with two gears, and the drive gear (receiving turning force directly from the motor) is larger than the driven gear, the latter rotates faster (and vice versa). Formula for calculation: gear ratio = T2/ T1, where T1 is the number of teeth of the first gear, T2 is the number of teeth of the second gear.

Steps

Gear ratio

Two gears

To determine the gear ratio, you must have at least two gears meshing with each other; This type of clutch is called a gear train.

• Typically, the first gear is the drive gear (attached to the motor shaft) and the second gear is the driven gear (attached to the load shaft). There can be as many gears as desired between the drive and driven gears. They are called intermediate.

1. Now let's look at a gear train with two gears. To determine the gear ratio, these gears must be meshed with each other (that is, their teeth mesh and one gear turns the other). For example, given a small drive gear (gear 1) and a large driven gear (gear 2). Count the number of teeth on the drive gear. The simplest way

   • find the gear ratio between two gears - compare the number of teeth on each of them. Start by determining the number of teeth on the drive gear. You can do this by hand or look at the gear markings.

2. For our example, let's say the smaller (drive) gear has 20 teeth.

   • Count the number of teeth on the driven gear.

3. In our example, let's say the large (driven) gear has 30 teeth. Divide the number of driven gear teeth by the number of drive gear teeth to calculate the gear ratio., Depending on the conditions of the problem, you can write the answer in the form decimal

common fraction

1. or as a ratio (x:y). More than two gears The gear train can include any number of a large number of

   • Consider the example above, but now the drive gear becomes a 7-tooth gear and the 20-tooth gear becomes an idler gear (the 30-tooth driven gear remains the same).

2. Divide the number of teeth on the driven gear by the number of teeth on the drive gear. Remember that when determining the ratio of a multi-gear gear train, it is important to know only the number of teeth on the driven gear and the number of teeth on the drive gear, that is, the idler gears do not affect the gear ratio.

   • In our example: 30/7 = 4.3. This means that the drive gear must make 4.3 revolutions for the driven (large) gear to make one revolution.

3. If necessary, find the gear ratios for the idler gears. To do this, start at the drive gear and work towards the driven gear. Whenever you re-calculate the gear ratio for idler gears, consider the previous gear as the drive gear (and divide the number of teeth on the driven gear by the number of teeth on the drive gear).

   • In our example, the gear ratios for the idler gear are: 20/7 = 2.9 and 30/20 = 1.5. Note that the ratio for the idler gear is different from the ratio for the entire gear train (4,3).
   • Also note that (20/7) × (30/20) = 4.3. That is, to calculate the gear ratio of the entire gear train, it is necessary to multiply the gear ratio values ​​for the intermediate gears.

Speed ​​calculation

1. Determine the rotation speed of the drive gear. Using the gear ratio and the rotation speed of the drive gear, you can easily calculate the rotation speed of the driven gear. Typically, rotation speed is measured in revolutions per minute (rpm).

   • Consider the example of a gear train described above (with three gears). Here the rotation speed of the drive gear is 130 rpm. Let's calculate the rotation speed of the driven gear.

• To see the principle of gear ratio in action, ride a bicycle! Note that it's easiest to go uphill when you have a small gear in the front and a large gear in the back. Although it's easier to pedal with a smaller gear, it will take a lot of spins to get the rear wheel to spin, meaning the bike's speed will be slower.
• The power required to move the load can be increased or decreased (relative to the engine power) by means of a gear train. When designing an engine, the gear ratio must be taken into account so that the engine power matches the nature of the future load. A boost system (in which the load shaft speed is higher than the engine speed) requires a motor that produces optimal power at lower drive shaft rotation speeds.
• On the other hand, a reduction system (in which the load shaft speed is lower than the engine speed) requires a motor that produces optimal power at high drive shaft speeds.