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Principles of Technology Waxahachie High School

Principles of Technology Waxahachie High School. Rate in Mechanical Systems PIC Chapter 3.1. PT TEKS. Rate in Mechanical Systems. Objectives: Define speed, velocity, and acceleration Explain the difference between speed and velocity

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Principles of Technology Waxahachie High School

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  1. Principles of TechnologyWaxahachie High School Rate in Mechanical Systems PIC Chapter 3.1 PT TEKS

  2. Rate in Mechanical Systems 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. Rate in Mechanical Systems The speed of an object is the ratio of distance in a given time. You can measure speed with a stop watch and a meter stick. Speed = Distance / time S = d/t This equation tells us the speed if the speed is constant

  4. Rate in Mechanical Systems If the speed varies, than we must find the average speed. Average speed = change in distance / change in time Vave = Δd / Δt

  5. Rate in Mechanical Systems You leave home and drive 100 miles east to your friend’s house. The trip takes 2 hours. On the return trip you drive through a rainstorm and it takes 3 hours driving the same 100 miles. Calculate the average speed driving to your friend’s house. Calculate the average speed driving from your friend’s house. Calculate the average speed for the entire trip.

  6. Rate in Mechanical Systems Calculate the average speed driving to your friend’s house. Vave= Δd / Δt Vave= 100 miles / 2 hrs Vave= 50 miles / hr

  7. Rate in Mechanical Systems Calculate the average speed driving from your friend’s house. Vave= Δd / Δt Vave= 100 miles / 3 hrs Vave= 33.3 miles/hr

  8. Rate in Mechanical Systems Calculate the average speed for the entire trip. Vave = Δd / Δt Vave = 200 miles / 5 hrs Vave = 40 miles/hr

  9. Rate in Mechanical Systems The speed at any one instant is called the instantaneous speed. The instantaneous speed can be found in a car with the speedometer.

  10. Rate in Mechanical Systems When we state the speed and direction of an object, we are stating the object’s Velocity. Velocity tells us direction and size so it is a vector. Speed tells us only size so it is a scalar.

  11. Rate in Mechanical Systems The vector that defines the distance and direction between two positions is called displacement. Displacement is like a short cut directly from one point to another.

  12. Rate in Mechanical Systems Average velocity = displacement / time V = d/t

  13. Rate in Mechanical Systems If you have a displacement of 145 km and your flight takes 2 hours, what is your average velocity? v = d/t v = 145 km / 2 hrs v = 72.5 km/hr

  14. Rate in Mechanical Systems The rate of change of an object’s velocity is the acceleration. (How fast you speed up or how fast you slow down) Acceleration is a vector.

  15. Rate in Mechanical Systems Average acceleration = change in velocity / time a = (Vf – Vi) / t

  16. Rate in Mechanical Systems A pilot increases the takeoff speed of an airplane from 20 ft/s to 200 ft/s in 30 seconds. What is the average acceleration? a = (Vf – Vi) / t a = (200 ft/s – 20 ft/s) / 30 s a = 180 ft/s / 30 s a = 6 ft/s2

  17. Rate in Mechanical Systems Speed and velocity are rates of linear motion. (in a straight line) Angular speed is a rate of rotational motion. The symbol for angular speed is ω, the Greek letter omega.

  18. Rate in Mechanical Systems Angular speed = angular displacement / time ω = Δθ/Δt Angle = # of turns x 2pi

  19. Rate in Mechanical Systems If we have a tire that rotates 30 times in 60 seconds, what is the angular speed of the tire? ω= Δθ/Δt θ= # of turns x 2 pi θ= 30 x 2 pi θ= 188.4 rad ω= 188.4 rad / 60 s ω= 3.14 rad / s

  20. Rate in Mechanical Systems Speed = radius x angular speed v = r x ω

  21. Rate in Mechanical Systems A vacuum cleaner has a shaft that is 1.5 inches in diameter and turns at an angular speed of 2000 rad/s, what is the speed of the belt connected to this shaft? ν = r x ω radius = diameter/2 r = 1.5 / 2 = .75 v = .75 in x 2000 rad/s v = 1500 in/s

  22. Rate in Mechanical Systems Change in angular speed = angular acceleration The angular acceleration is the ratio of the change in angular speed to the time interval.

  23. Rate in Mechanical Systems Angular acceleration (α - alpha) = change in angular speed / time α = (ωf – ωi) / t

  24. Rate in Mechanical Systems A car’s brake is applied to a wheel for 5 seconds, reducing the wheel’s angular speed from 220 rad/sec to 180 rad/sec. What is the angular acceleration? α = (ωf– ωi) / t α = (180 rad/s – 220 rad/s) / 5 s α = -40 rad/s / 5 s α = -8 rad/s2

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