DEGREES OF COMPARISON OF ADJECTIVES In English, as in Russian, ...
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1 2 Uniform movement along a circle is such a movement in which a material point passes equal arcs of a circle in equal intervals of time. Uniform movement along a circle Solving problems 10 3 4 5 6 7 8 9 Lyakhovich E.Yu.
Orbital period 2 1 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH No. 3", Nizhnekamsk The time of one revolution around the circle is called the period of rotation T N is the number of revolutions made during the time t . The unit of rotation frequency is 1 revolution per second (1 s -1)
3 2 10 1 4 5 6 7 8 9 Lyakhovich E.Yu.
4 2 10 3 1 5 6 7 8 9 Lyakhovich E.Yu.
5 2 10 3 4 1 6 7 8 9 Lyakhovich E.Yu.
6 2 10 3 4 5 1 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH №3", Nizhnekamsk Problem. What is the linear speed of the points on the wheel rim of a steam turbine with a wheel diameter of 1 m and a speed of 300 rpm? Show Solution
7 2 10 3 4 5 6 1 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH №3", Nizhnekamsk Problem. How many times will the centripetal acceleration of a body change if it moves uniformly along a circle of twice the radius with the same angular velocity? Show Solution
8 2 10 3 4 5 6 7 1 9 Lyakhovich E.Yu., MBVSOU "VSOSH №3", Nizhnekamsk Problem. The angular velocity of the fan blades is 20π rad/s. Find the number of revolutions in 30 min. Show Solution
1 Option 2 Option 1. The angular velocity of the fan blades is 20π rad/s. Find the number of revolutions in 30 min. 2. Aircraft propeller speed 1500 rpm. How many revolutions will the propeller make on a path of 90 km at a flight speed of 180 km/h 2 . The locomotive moves at a speed of 60 km/h. How many revolutions per second does its wheels make if their radius is 50 cm? one . At the turn, the tram car moves with a constant modulo speed of 5 m/s. What is its centripetal acceleration, if the radius of curvature of the path is 50 m. 9 2 10 3 4 5 6 7 8 1 Lyakhovich E.Yu.
ANSWERS 1 Option 2 Option 1 . 18000.2. 45000 2 . 5.31 1 . 0.5 m/s 2 . 1 2 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH No. 3", Nizhnekamsk
1 2 10 3 4 5 6 7 8 9 Lyakhovich E.Yu., MBVSOU "VSOSH №3", Nizhnekamsk Show solution
On the topic: methodological developments, presentations and notes
Lesson for solving problems on the topic "Dynamics of motion in a circle." In the process of solving problems in groups, mutual learning of students takes place ....
A lesson in learning a new topic using a presentation, videos ....
The work is intended for students of grade 10, presented in two versions. Tasks for knowledge of definitions, graphic tasks and assignments for correspondence ....
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Movement in a circle (closed track) Savchenko Elena Mikhailovna, mathematics teacher of the highest qualification category. Municipal educational institution gymnasium No. 1, Polyarnye Zori, Murmansk region State (final) certification Training modules for distance self-training XIV All-Russian competition methodological developments"One Hundred Friends"
If two cyclists simultaneously start moving in a circle in one direction with speeds v 1 and v 2, respectively (v 1 > v 2, respectively), then the 1st cyclist approaches 2 with speed v 1 - v 2. At the moment when the 1st cyclist catches up with the 2nd for the first time, he covers the distance by one lap more. Continue Show At the moment when the 1st cyclist catches up with the 2nd for the second time, he covers the distance for two laps and more, and so on.
1 2 1. From one point of the circular track, the length of which is 15 km, two cars started simultaneously in the same direction. The speed of the first car is 60 km/h, the speed of the second is 80 km/h. How many minutes will pass from the moment of the start before the first car is exactly 1 lap ahead of the second? 1 red 2 green 60 80 v, km/h 15 km less (1 lap) Equation: Answer: 45 x we get in hours. Don't forget to convert to minutes. t , h x x S, km 60x 80x Show
2 1 2. From one point of the circular track, the length of which is 10 km, two cars started simultaneously in the same direction. The speed of the first car is 90 km/h, and 40 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h. 1 car 2 cars 90 x v, km/h per 10 km more (1 lap) Answer: 75 t , h 2 3 2 3 S, km 2 3 90 2 3 x Equation: Show
3. Two motorcyclists start simultaneously in the same direction from two diametrically opposite points of a circular track, the length of which is 14 km. In how many minutes will the motorcyclists catch up for the first time if the speed of one of them is 21 km/h more than the speed of the other? 1 red 2 blue x x + 21 v, km/h 7 km less (half circle) Equation: Answer: 20 t we get in hours. Don't forget to convert to minutes. t , h t t S, km t x t(x +21) How many laps each motorcyclist has driven is not important to us. It is important that blue has traveled half a circle more to the meeting point, i.e. at 7 km. Another way is in the comments. Show
start finish 2 1 2 1 1 2 2 1 1 2 Let the full circle be 1 part. 4. Ski competitions are held on a circular track. The first skier completes one lap 2 minutes faster than the second and an hour later he is exactly one lap ahead of the second. How many minutes does the second skier complete one lap? Show
4. Ski competitions are held on a circular track. The first skier completes one lap 2 minutes faster than the second and an hour later he is exactly one lap ahead of the second. How many minutes does the second skier complete one lap? 1 lap more Answer: 10 1 skier 2 skier v, lap/min t , min 60 60 S, km x x+2 1 1 t , min 1 skier 2 skier S, part v, part/min 1 x+2 1 x 1 x + 2 1 x 60 x 60 x + 2 First, let's express the speed of each skier. Let the 1st skier complete a full circle in x minutes. The second one is 2 minutes longer, i.e. x+2. 60 x 60 x + 2 - = 1 This condition will help to enter x ...
5. From one point of the circular track, the length of which is 14 km, two cars started simultaneously in the same direction. The speed of the first car is 80 km/h, and 40 minutes after the start it was one lap ahead of the second car. Find the speed of the second car. Give your answer in km/h. 1 yellow 2 blue S, km 80 x v, km / h t , h 2 3 2 3 2 3 80 2 3 x 14 km more (1 circle) Equation: You could first find the speed in pursuit: 80 - x Then the equation will be look like this: v S t Answer: 59 You can press the button several times. How many laps each car drove is not important to us. It is important that the yellow car drove 1 more lap, i.e. at 14 km. Show 1 2
6. A cyclist left point A of the circular track, and after 30 minutes a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the track is 30 km. Give your answer in km/h. 1 motorcycle. 2 bike. S, km x y v, km/h t , h 1 6 2 3 2 3 y 1 equation: 1 6 x = Show 1 meeting. The cyclist was up to 1 meeting 40 minutes (2/3 h), the motorcyclist 10 min (1/6 h). And the distance during this time they traveled equal.
6. A cyclist left point A of the circular track, and after 30 minutes a motorcyclist followed him. 10 minutes after departure, he caught up with the cyclist for the first time, and 30 minutes after that he caught up with him for the second time. Find the speed of the motorcyclist if the length of the track is 30 km. Give your answer in km/h. 1 motorcycle. 2 bike. S, km x y v, km/h t , h 1 2 1 2 1 2 y 30 km more (1 lap) Equation 2: Answer 80 1 2 x Desired value - x Show (2) 2nd meeting. The cyclist and the motorcyclist were on their way to the 2nd meeting in 30 min (1/2 h). And the distance during this time the motorcyclist traveled 1 lap more.
7. Clock with hands shows 8 hours 00 minutes. After how many minutes will the minute hand align with the hour hand for the fourth time? minute hour x S, lap v, lap/h t , h 1 1 12 x 1x 1 12 x over laps 2 3 3 1x – = 1 12 x 2 3 3 Answer: 240 min 2 3 1 3 For the first time the minute hand you have to go a circle more to catch up with the minute hand. 2nd time - 1 more lap more. 3rd time - 1 more round. 4th time - 1 more lap more. Total 2 3 laps over 2 3 3
6 12 1 2 9 11 10 8 7 4 5 3 Show (4) The first time the minute hand needs to go one more lap to catch up with the minute hand. 2nd time - 1 more lap more. 3rd time - 1 more round. 4th time - 1 more lap more. Total 2 3 laps more than 2 3 3 Check Another way is in the comments.
USE 2010. Mathematics. Task B12. Edited by A. L. Semenov and I. V. Yashchenko http://www.2x2abc.com/forum/users/2010/B12.pdf An open bank of assignments in mathematics. USE 2011 http://mathege.ru/or/ege/Main.html Drawings by the author http://le-savchen.ucoz.ru/index/0-67 Skier http://officeimg.vo.msecnd.net/en -us/images/MH900282779.gif Materials published on the author's website "Website of the teacher of mathematics" Section "Preparation for the Unified State Examination". Task B12. http://le-savchen.ucoz.ru/publ/17
