PPT-Equations of 1-D Motion

Equations for uniform acceleration Where s is displacement m v is the final velocity m s 1 u is the initial velocity m s 1 a is the acceleration m s 2 . Molecular dynamics in the . microcanonical. (NVE) ensemble:. . the . Verlet. algorithm. Equations of motion for atomic systems in . cartesian. coordinates. Classical. . equation. of . motion. . Outline. Time Derivatives & Vector Notation. Differential Equations of Continuity. Momentum Transfer Equations. Introduction. FLUID. In order to calculate forces exerted by a moving fluid as well as the consequent transport effects, the dynamics of flow must be described mathematically . Purpose:. This chapter introduces the dynamics of mechanisms.  A robot can be treated as a set of linked rigid bodies. Each link body experiences the motion dynamics contributed by its own joint motor plus the cumulative effect of the other links that form a dynamic chain. This means that we must recursively accumulate the net dynamics by moving from one link to the next. This approach is referred to as the Newton-Euler recursive equations. The equation types are distinguished as Newton for force equations and as Euler for moment equations. . 2D Motion. Moving Motion Forward. Velocity, Displacement and Acceleration are VECTORS. Vectors have magnitude AND direction. So far, direction has been positive and negative. Motion with Vectors. Motion concepts combine with Vector concepts to allow us to represent motion in multiple directions simultaneously. Chapter 2. Kinematics. .  . motion.. Dynamics .  . forces impacting motion.. Mechanics . .  . kinematics & dynamics. 1. 2.1 Displacement. 2. 2.1 Displacement. 3. instantaneous . velocity . Re-Made Version. Coupled Motion. Coupled motion problems are problems in which the movement of one object directly impacts the motion of another object.. We have already briefly covered this topic when talking about pulleys.. Kinematic Equations. Measuring Techniques. Assess. . Statements . 2.1.1 – . 2.1.5, . 2.1.7 – . 2.1.10. Due on Wednesday, . Oct. 29. Uniform Accelerated Motion. Acceleration:. . The rate at which an object’s velocity changes. : Lecture. 7. (ME EN 7960-008). Prof.. Rob Stoll. Department of Mechanical Engineering. University of Utah. Spring 2011. Equations of Motion. . Incompressible flow:. . g. eneral scalar (. Sc. =Schmidt #). Equations of Motion for Constant Resultant Force. Also called ….. because………. …acceleration and resultant force are directly proportional. . s. uvat. equations. Also called ….. (unhelpfully). Honors Trigonometry. Chapter 8 . Section 6. What is projectile motion?. What variables can you control?. What sports use projectile motion?. Ovida. . Fentz. hits a baseball so that it travels at a speed of 120 feet per second and at an angle of 30 degrees to the horizontal. Assume his bat contacts the ball at a height of 3 ft above the ground.. Nature of science: . Observations: The ideas of motion are fundamental to many areas of physics, providing a link to the consideration of forces and their implication. The kinematic equations for uniform acceleration were developed through careful observations of the natural world.. Sub units. Reference Frames and Displacement. Average Velocity. Instantaneous Velocity. Acceleration. Motion at Constant Acceleration. Solving Problems. Falling Objects. Graphical Analysis of Linear Motion. 1. Changing Units. Speed of a car is 80 miles/hour. What is it in m/s. Multiply by 1 so units cancel and correct units are left. In units of m/s: {80 miles * (5280 feet/mile)*(1 m/3.28 feet)}/hour. Motion in Two Dimensions. Using + or – signs is not always sufficient to fully describe motion in more than one dimension. Vectors can be used to more fully describe motion. Still interested in displacement, velocity, and acceleration.