1. Rotational Equilibrium and Dynamics
Simple Machines

2. Simple Machines Machines multiply and redirect force
Simple machines – one of the six basic types of machines of which all other machines are composed
Two families of simple machines:
Levers and Inclined planes

3. The Lever Family Three groups of machines in the lever family Levers
Pulleys
Wheel and Axle

4. Levers "Give me a place to stand and I will move the earth.”
Archimedes On the lever in Pappus Synagoge
Levers have a rigid arm that turns around a fulcrum
Force is transmitted from one part of the arm to another

5. Levers Three classes of lever
Based on the location of the fulcrum and input and output forces
First-class lever – has the fulcrum between the input and output forces
Examples: claw hammer, see-saw
A pair of pliers is made of two first-class levers

6. Levers

7. Levers
Second class-levers – the output force is in the middle between the fulcrum and the input force
Examples: Wheelbarrow, nutcrackers, hinged doors

8. Levers

9. Levers
Third-class levers – the input force is between the fulcrum and the output force
Example: human forearm

10. Levers

11. Pulleys Pulleys are modified levers
Used to lift objects
The point in the middle of the pulley is like the fulcrum in a lever
The rest of the pulley is like the arm
Multiple pulleys are sometimes called a block-and-tackle

12. Pulleys

13. Pulleys

14. Pulleys

15. Wheel and Axle
Wheel and Axle – a lever or pulley (the wheel) connected to a shaft (the axle)
Examples: steering wheel, screwdrivers

16. Inclined Plane Family
Three types of machines in the inclined plane family
Inclined plane
Wedge
Screw

17. Inclined Planes
Inclined planes – the input force is directed parallel to the ramp
The output force is directed up

18. Wedge Wedge – acts like two inclined planes back-to-back
Turns a single downward force into two forces directed out to the sides
Example: axe head, nails

19. Screw Screw – an inclined plane wrapped around a cylinder
Steeper threads require more force to tighten
Examples: jar lids, wood screws, spiral staircases

20. Compound Machines
Compound machine – a machine made up of more than one simple machine
Scissors – two first class levers joined at a common fulcrum with each arm having a wedge
Car jack – lever with a screw

21. Machines and Torque
Input torque equals output torque
τin = τout

22. Machines and Mechanical Advantage
Machines multiply and redirect force
Changes the direction of an input force
Increases the output force by changing the distance over which the force is applied
Does not change the amount of work done

23. Machines and Mechanical Advantage
Mechanical advantage – a quantity that measures how much a machine multiplies force or distance
Mechanical advantage = output force
input force
Mechanical advantage = input distance
output distance
MA = Fo = di
Fi = do

24. Machines and Mechanical Advantage
Mechanical advantage greater than one multiplies the input force
Mechanical advantage less than one increases distance and speed
Mechanical advantage does not have any units

25. Efficiency of Machines
Not all work done by a machine is useful work
Some of the energy is lost to sound or heat
No machine is perfect
There are no perpetual motion machines

26. Efficiency of Machines
Efficiency – a quality, usually expressed as a percentage, that measures the ratio of useful work output to work input
Efficiency = (useful work output)/(work input)*100%
Eff = Wo/WI*100%