Mechanical Rate (a.k.a. Motion)

TEKS TLW knows the laws governing motion (TEKS 5) TEKS 5.A - Analyze examples of uniform and accelerated motion – including linear, projectile, & circular TEKS 5.B - Generate and interpret graphs describing motion including the use of real-time technology TEKS 5.C – Formulate the effects of forces on motion of objects TEKS 5.D – Develop and interpret a free-body diagram for force analysis TEKS 5.E – Identify and describe motion relative to different frames of reference

Lesson Plan Objectives Identify and describe motion relative to different frames of reference – such as heights and orbits Use real-time technology (photo-gates, ramps, stop watchers, etc.) in hands-on labs Prepare and interpret graphs from data collected on linear, projectile, and circular motion Define Speed, velocity, and acceleration. Explain the difference between speed and velocity. Explain the difference between velocity and acceleration. Use speed, velocity, and acceleration to solve problems involving linear (one-dimensional) motion.

Lesson Plan Objectives Use speed, velocity, and acceleration to solve problems involving projectile motion Define angular speed and angular acceleration. Use angular speed and angular acceleration to solve problems involving rotational motion. Create and use free-body diagrams to analyze force scenarios

Speed Speed is the ratio between the distance traveled and the elapsed time. (scalar quantity) Distance traveled (  d) Time interval (  t) Speed = Examples of units to use: m/sec, km/hr, ft/sec, or miles/hr

Average Speed When speed varies between point A and B Distance traveled (  d) Time interval (  t) Average Speed = dd tt s avg = = d 2 – d 1 t 2 –t 1 d 2 = final distance (d f ) d 1 = initial starting point (d i ) t 2 = final time (t f ) t 1 = initial time (t i )

Velocity A vector quantity giving the speed (magnitude) and direction of travel. displacement time Velocity = dd tt v avg =

Acceleration Describes the rate of change of an object’s velocity Velocity change (  v) Time interval (  t) Average Acceleration = vv tt a avg == v 2 – v 1 t 2 –t 1 Negative acceleration is called deceleration v 2 = final velocity (v f ) v 1 = initial velocity (v i ) t 2 = final time (t f ) t 1 = initial time (t i )

Projectile Motion

Angular Speed Rate of rotational motion. angular displacement (  ) time interval (  t) (  ) = Angular Speed omega 1 revolution = 360º = 2  radians radians or revolutions

Angular Acceleration Ration of the change in angular speed to the time interval. Angular speed change (  ) Time interval (  t) Angular Acceleration =  tt a ==  2 –  1 t 2 –t 1

Summary Speed is a measure of the rate of motion of an object. It is the ratio of distance traveled to the time interval. Speed is a scalar quantity. Velocity is the ratio of displacement to the time interval. Velocity and displacement are vector quantities. Speed is the magnitude of velocity. Acceleration is a measure of the rate of change of an object’s velocity. It is the ratio of change in velocity to the time interval. Angular speed is a measure of the rate of rotational motion of an object. It is the ratio of angular displacement to time interval. Angular acceleration is a measure of the rate of change of an object’s angular speed. It is the ratio of change in angular speed to the time interval.