1. Mechanical Rate

2. Objectives 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 motion. Define angular speed and angular acceleration. Use angular speed and angular acceleration to solve problems involving rotational motion.

3. Speed Speed is the ratio between the distance traveled and the elapsed time. (scalar quantity) Distance traveled (  d) Time interval (  t) Speed = [m/sec] [km/hr] [ft/sec] [miles/hr]

4. Average Speed When speed varies between point A and B Distance traveled (  d) Time interval (  t) Average Speed = dd tt v avg == d 2 – d 1 t 2 –t 1

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

6. 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

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

8. 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

9. 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.