1. Chap 3 – Sec 1 Rate in Mechanical Systems

2. Objectives Define speed, velocity & acceleration. Explain the difference between speed & velocity. Explain the difference between velocity and acceleration. Define angular speed & angular acceleration. Solve problems in linear & angular motion.

3. Speed Speed equals the distance traveled divided by the time it took to travel it. Speed = distance / time = d/t Average speed is the total distance traveled divided by the total time. Instantaneous speed is the speed at a given instant in time. Ex – speedometer reading.

4. Velocity Velocity is a vector quantity. It has a direction & magnitude. The magnitude of the velocity vector is speed. Example – 50 mph is a speed. 50 mph due north is a vector.

5. Acceleration Acceleration is the change in velocity divided by the change in time, a = v / t Any change in the velocity vector is an acceleration. Since velocity is a vector, a change in the direction of the vector is an acceleration. A car has three accelerators; gas pedal, brake & steering wheel.

6. Units Velocity (speed) – English – ft/s, mph; SI – m/s, kph Acceleration – ft/s 2 ; SI – m/s 2

7. Angular velocity Angular velocity is the change in angle over change in time,  =  /t Units are radians/second; rad/s Sometimes expressed in revolutions per minute (RPM).

8. Angular acceleration Angular acceleration is the change in angular velocity over time,  =  /t. Units are rad/s 2.

9. Graphing Speed

10. On a distance – time graph: The slope of the graph is the speed. Slope = rise / run

11. Graphing Speed

12. Speed = slope Slope = rise / run Rise = 8 – 2 = 6 Run = 4 – 1 = 3 Speed = 6/3 = 2 m/s

13. Velocity time graph

14. In a velocity – time graph Slope = acceleration

15. Velocity time graph

16. Acceleration = slope Slope = rise / run Rise = 12 – 3 = 9 Run = 4 – 1 = 3 Acceleration = 9/3 = 3 m/s/s = 3 m/s 2

17. Summary Speed is a measure of the rate of motion of an object. It is distance traveled divided by time. Speed is a scalar quantity. Velocity is displacement divided by time. Velocity is a vector quantity. The magnitude of the velocity vector is speed. Acceleration is the rate of change of an object’s velocity. It is velocity divided by time. Angular speed is the measure of an object’s rotational motion. It is the change in angle divided by time. Angular acceleration is the rate of change of an object’s angular velocity. It is angular velocity divided by time.