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Kinematics Study of Motion

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Kinematics Study of Motion Kinematics Study of motion Kinematics is the branch of physics that describes the motion of objects, but it is not interested in its causes. Itziar Izurieta (2018 october) Index: 1. What is motion? ............................................................................................ 1 1.1. Relativity of motion ................................................................................................................................ 1 1.2.Frame of reference: Cartesian coordinate system ....................................................................................................................................................................... 1 1.3. Position and trajectory .......................................................................................................................... 2 1.4.Travelled distance and displacement ....................................................................................................................................................................... 3 2. Quantities of motion: Speed and velocity .............................................. 4 2.1. Average and instantaneous speed ............................................................ 4 2.2. Average and instantaneous velocity ........................................................ 7 3. Uniform linear motion ................................................................................. 9 3.1. Distance-time graph .................................................................................. 10 3.2. Velocity-time graph .................................................................................... 11 4. Velocity change: Acceleration ................................................................ 14 5. Uniformly accelerated linear motion (UALM) ..................................... 16 5.1. Graphs in uniformly accelerated motion ............................................... 17 5.2. Vertical motion due to gravity: Free fall. .............................................. 19 Common mistakes and misconceptions ...................................................................................................... 20 Vocabulary .......................................................................................................... 31 1- What is motion? 1.1- Relativity of motion 1.2- Position and trajectory 1.3- Displacement and travelled distance 2- Speed 2.1- Average speed and instantaneous speed. 2.2- Average velocity and instantaneous velocity. 2.3- Uniform linear motion: graphs and equations 3- Velocity change 3.1- Acceleration. 3.2- Uniformly accelerated linear motion 3.3- Circular motion. 1. What is motion? Even when we are standing still on the Earth we are actually travelling at extremely high speeds. This is because the Earth is constantly spinning (rotating) on its axis and travelling around the Sun. Even the Sun isn’t standing still; it is travelling at an incredibly high speed around our galaxy. In physics, motion is the study of how something moves, whether it is a planet moving around the Sun or a snowboarder flying through the air. An object’s motion is usually described in terms of its velocity and acceleration, and its motion only changes if a force or several forces act on it. 1.1. Relativity of motion How can we know, in an objective way, what is in motion? And what is stationary? How can we know if something is moving or still? Motion is the change in position of an object with respect to another one: it is the change of position that an object goes through as time goes by relative to a reference system that we take as still and fixed (relative to a fixed reference that we take as stationary). Taking this definition into account motion is relative. Each object in the universe is moving relative to the rest. An object may appear to have one motion to one observer and a different motion to a second observer. For example, if we are travelling in a car, we are still relative to the car (if the car is our reference system), but we are in motion relative to the road or to any tree at one side of the road (if the road or the tree are our system of reference). So, motion is a relative concept, we measure it relative to an object or an observer that we consider not to be moving. We describe motion in terms of position, time, displacement, velocity and acceleration. A body that does not move is said to be at rest, motionless, immobile, stationaryor to have a constant time- invariant position. ** In order to simplify the study of motion and unless otherwise stated, we consider every object in the universe as a point, known as a material point. 1.2. Frame of reference: Cartesian coordinate system The reference system is the frame of reference, also called reference frame. A framework that is used for the observation and mathematical description of physical phenomena and the formulation of physical laws, usually consisting of an observer, a coordinate system, and a clock or clocks assigning times at positions with respect to the coordinate system. In a Cartesian coordinate system, the way to locate objects is based on a set of perpendicular axes that intersect at the orgigin. To locate an object in space we need a frame of reference with three axes. But, this year, however, we will study movemente in a plane and two axes will be enough. Three dimension Two dimension Kinematics (I.I) 1 1.3. Position and trajectory Trajectory (or path): this is the path that a moving object follows through space over time. A trajectory may be linear (straight) or curved. This line is obtained by joining all the positions that an object takes in its motion. Position: this is the point where an object is located at any moment relative to a system of reference. For example, if we use a road as a system of reference and any point, O, in this road as the origin, we know the position of a car if we know the distance till the origin. ¿? ? There are many types of motion: Depending on the shape of the path, a given motion is classified: Linear when it is a straight line Curvilinear if it is not a straight line. In the special case of movement along a circumference, we call a circular motion. Kinematics (I.I) 2 This year we will look more closely at linear motion and circular motion, fron which , in the future, you will be able to study more complex motion. 1.4. Travelled distance and displacement . Travelled distance, s ( is a greek letter to express change), is the length of the path the object or body has described: s = s - so If the path is straight and parallel to the X axis, we use x to express the distance travelled. If the path is straight and parallel to the Y axis, we use y to express the distance travelled. In other cases (round, elliptic paths...) we use s to express the distance travelled. Displacement is a vector quantity. Displacement is distance in a given direction. It is a vector quantity (it has a direction associated with it). To define a vector quantity it is necessary to use its size (value), its units, its direction and sometimes also its origin. It is the vector from the starting point to the end point. It is obtained by making the subtraction of the final and the initial position. If we use only one of the axis, we don’t need to use the vector expression and the signal of the subtraction will give us information about the direction of the motion in the same way. Displacement from the initial position (1,3) m to (4,2) m. The curved line is thetrajectory between these two points If trajectory is straight travelled distance = displacement The SI unit of distance and displacement is the meter [m]. -2 -1 0 1 2 3 4 5 6 7 a) From 1 m to 5 m: x = 5-1 = 4 m to the right Displacement = Travelled distance b) From 5 m to 6 m: x = 6-5 = 1 m to the right Displacement = Travelled distance c) From 6 m to -1 m: x = -1 -6 = -7 m to the left |Displacement| = Travelled distance d) From -1 m to – 6 m: x = 6-(-1) = 7 m to the left |Displacement| = Travelled distance Kinematics (I.I) 3 Activities: 1. A cyclist has travelled around a semicircular curve of 50 m in radius. How much distance, s, has he travelled? And what displacement, x, has he travelled? Do they have the same value? Why? Draw it 2. The initial position of a moving object is -400 m and the final one is 13 km. Knowing that its path was straight, what distance has he travelled? Draw the displacement vector. 3. Give an example of an object that has a displacement, x, of 0 after having moved. 4. A tank travels 12 km to the North, then it turns East and travels 5 km. What is the total distance travelled by the tank? What is the displacement of the tank? 5. A toy train moves along a circular path of radius 20 cm as shown in the picture. What is the distance and displacement travelled when the train a) moves from O to P? b) moves from O to and then back to O? 2. Quantities of motion: Speed and velocity 2.1. Average and instantaneous speed Cars have speedometers. But how can you tell how fast you are going on your bike? Most bicycles do not have speedometers, so you cannot measure your speed directly. But you can time how long it takes to cycle between two places, two lamp-posts, for example. And you can measure how far you have cycled: the distance between the two lamp-posts. Then you can work out the average speed. Speed is the rate of change of distance with respect to time. The symbol for speed is v. Speed is a scalar quantity. Its unit is the meter per second (m.s-1 or m/s). It can be measured in kilometres per hour (miles per hour in England!).
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