KINEMATICS-notes.pdf

KINEMATICS: A DESCRIPTION OF MOTION MECHANICS Mechanics is a branch of physics that deals with the motion of objects and the forces that change. It also deals with the particles that are moving either with less velocity or they are at rest. It is also called Classical M...

KINEMATICS: A DESCRIPTION OF MOTION MECHANICS Mechanics is a branch of physics that deals with the motion of objects and the forces that change. It also deals with the particles that are moving either with less velocity or they are at rest. It is also called Classical Mechanics or LESSON 5: MOTION IN A STRAIGHT LINE Newtonian Mechanics. Mechanics is of vital importance in describing motion of material SPEED AND VELOCITY bodies, such as planets, rockets, falling objects, Galileo Galilei, the founder of modern and baseballs. experimental science said that the motion of Areas of Mechanics moving objects maybe described in terms of time rates of change. Therefore, the rates that Kinematics describes the quantitative describe motion are speed, velocity, and description of motion such as the rate at acceleration. which the particles are moving (velocity) and the rate at which their velocity is Speed and velocity use the terms changing (acceleration). distance and displacement. Distance is a scalar Dynamics deals with forces and their quantity which represents the total path length. effect on motion. It also includes the Displacement is the straight-line distance study of the effect of torques in motion. between the starting and end points. Statics deals with the study of forces Speed is a scalar quantity which specifies acting on bodies at rest. When in static magnitude of the rate of motion without equilibrium, the system is either at rest, reference to the direction of motion. It can also or its center of mass at constant velocity. be defined as the distance traveled per unit of MOTION time. Motion is the displacement of an object 𝒅 𝒗= in relation to objects that are considered to be 𝒕 stationary. Motion can also be defined as the In symbols, continuous change of position with respect to a certain reference point. Speed can be expressed by the units cm/s, m/s, km/h, ft/s, mi/h, etc. TYPES OF MOTION Average speed is the total distance Rectilinear/Translatory motion is traveled divided by the total time to travel that the motion of a body along a straight line. distance. Linear motion is the most basic of all motions. According to Newton's First law 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑒𝑑 of Motion, objects that are not subjected ave. speed = to forces will continue to move uniformly 𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑜 𝑡𝑟𝑎𝑣𝑒𝑙 𝑡ℎ𝑎𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑑 in a straight line indefinitely. An example =𝑣= 𝑡 of linear motion is that of a ball thrown straight up and falling back straight down. Velocity is the total displacement Curvilinear/Rotational motion is the covered in a given time interval. It can also be motion along a circular path. An example defined as a speed in a given direction. is a car negotiating a curve. Vibrational motion is a to and fro motion of a body. An example is a moving pendulum. ACCELERATION Acceleration is a vector quantity which Problem 2 describes how velocity changes with time. During a race, a sprinter increases from 5.0 m/s Mathematically, acceleration is expressed as to 7.5 m/s over a period of 1.25s. What is the 𝒗𝒇 − 𝒗𝒊 sprinter's average acceleration during this 𝒂= 𝒕𝒇 − 𝒕𝒊 period? Where Given: 𝑣𝑖 =5.0 m/s 𝑣𝑓 = final velocity 𝑣𝑖 = initial velocity 𝑣𝑓 = 7.5 m/s 𝑡𝑓 = final time 𝑡𝑖 = initial time t = 1.25 s When an object starts moving from rest, the Find. Ave. acceleration equation becomes Solution: 𝑣𝑓 − 𝑣𝑖 𝒗 𝑎= 𝒂= 𝑡 𝒕 7.5 𝑚/𝑠 − 5.0 𝑚/𝑠 𝑎= 1.25 𝑠 Calculating acceleration involves dividing 2.5 𝑚/𝑠 velocity by time or in terms of units, dividing 𝑎= 1.25 𝑠 meters per second [m/s] by second [s]. Dividing 𝑎 = 2 𝑚/𝑠 2 distance by time twice is the same as dividing distance by the square of time. Thus, the SI unit of acceleration is the meter per second squared. 𝒎 𝒎/𝒔 𝒎 𝟏 = = 𝒙 𝒔𝟐 𝒔 𝒔 𝒔 Acceleration can also be expressed in units such as m/s2, km/h2, km/h/s. A moving object is accelerating when (1) the velocity is changing (increasing or decreasing); (2) the direction is changing; and (3) both velocity and direction is changing. Acceleration can be positive or negative. Deceleration indicates negative acceleration. Problem 1 As a shuttle bus comes to a normal stop, it slows from 9.0m/s to 0.0m/s in 5.0s. Find the average acceleration of the bus. Given: initial velocity = 9.0 m/s, final velocity = 0.0, time = 5.0 s Find: ave. acceleration Solution: 𝑣𝑓 − 𝑣𝑖 𝑎= 𝑡 0 − 9.0 𝑚/𝑠 𝑎= 5𝑠 𝑎 = −1.8 𝑚/𝑠 2