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Republic of Kazakhstan Republic of Kazakhstan Ministry of Education and Science Kazakh-British Technical University Faculty of Power and Oil and Gas Industry Physical Engineering Department Physics 1 Voronkov Vladimir Vasilyevich

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Physics 1 Mechacnics Molecular physics and Thermodynamics Electricity Magnetism

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Lecture 1 SUBJECTS: Mechanics Kinematics Rectilinear motion Projectile motion Uniform circular motion

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Mechanics Mechanics is the science of motion and its cause. Kinematics is the mathematical description of motion.

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Main terms of Kinematics Displacement is the change in the position of an object. one-dimensional: ∆x= x2 - x1 many-dimensional: Average velocity is the distance traveled per unit of time: Instantaneous velocity is the velocity at infinitely small interval: or the same

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Average acceleration is the total change in velocity per unit of time: Average acceleration is the total change in velocity per unit of time: Instantaneous acceleration is the change in velocity per unit of time at infinitely small time: Gravitational motion is the motion when gravitational acceleration g=9.8 m/s2 takes part. For example: rocket motion.

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Displacement at constant acceleration in rectilinear motion : Displacement at constant acceleration in rectilinear motion : Where r0 and V0 is initial displacement and velocity at t=0, a is constant acceleration.

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Rectilinear motion in graphics A) Object stands still. B) Object moves with constant speed.

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Another example of rectilinear motion

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The car motion in table The car motion in table

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Velocity and acceleration

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Projectile motion is a gravitational motion but the object has no its own acceleration. So the motion goes with constant gravitational acceleration. For example: cannonball motion. Projectile motion is a gravitational motion but the object has no its own acceleration. So the motion goes with constant gravitational acceleration. For example: cannonball motion. Usual method for solving projectile motion problems: Separate the motion into two parts: vertical and horizontal: so we have: two coordinates x and y two velocities Vx and Vy one acceleration ay =-g, and ax=0

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Then one should determine the elevation angle Θ0 - the initial angle to horizon. Then one should determine the elevation angle Θ0 - the initial angle to horizon. So the trajectory of an object in the gravitational field can be described as following: x= V0CosΘ0 t, y= V0SinΘ0 t – gt2/2. Let’s designate R as the range the object travels from zero height (y=0) till its fall (y=0 again) then we can calculate it as R=V02Sin(2Θ0)/g. Flight time t: it’s easy (using the equation dy/dt = 0) to find that the time of ascent is V0SinΘ0/g, then the full flight time is double: tflight= 2V0SinΘ0/g. Using the flight time one can find: the maximal height, the range of flight (the maximum range of flight from zero height (y=0) till the fall of the object (y=0 again)).

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Circular uniform motion Uniform circular motion is performed with constant speed along a circular path. Circular motion is a special case of motion on a plane. Its coordinates is angular coordinate φ and radius r. The angular speed is defined as: The linear speed relates to the angular speed as: Period T is the time of one full revolution: T= 

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Units in SI Displacement x,y m Velocity V m/s Acceleration a,g m/s2 Angle φ rad Angular speed  rad/s Period T s

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Read before the next Lecture Fishbane Chapters 4,5 pp.87-150 Russian equivalents: Трофимова Т.И. Курс физики. Глава 2 Динамика материальной точки. Савельев И.В. Курс общей физики. Т.1. Глава 2 Динамика материальной точки.