PHYS16 – Lecture 24

1. PHYS16 – Lecture 24 Simple Machines II and Static Equilibrium November 3, 2010

2. Review of last time…

3. Practice Question 1 • In a spin, why do ice skaters decrease their ang. velocity when they hold their arms out? • It decreases ang. momentum. • It decreases rot. inertia. • It increases rot. inertia. • It increases the centripetal force. • None of the above. Kristi Yamaguchi http://www.corbisimages.com/images/67/7760610C-6DF3-4A39-ACD6-C3CDEFF73296/PN015983.jpg

4. Practice Question 2 • A lawn tractor tire turns at 65.0 rpm and has a radius of 13.0 cm. Find the linear speed of the tractor in m/s. • 0.141 m/s • 0.885 m/s • 88.5 m/s • 186 m/s

5. Practice Question 3 • A ball attached to the end of a string is swung in a vertical circle. The angular momentum of the ball at the top of the circular path is: • > ang. momentum at the bottom • = ang. momentum at the bottom • < ang. momentum at the bottom

6. Practice Question 4 • The turbine of a jet engine has a moment of inertia of 25 kg∙m2. If the turbine is accelerated uniformly from rest to an angular speed of 150 rad/s in a time of 25 s, what is the torque?

7. This Week • Simple Machines II – gears, belts, and levers • Static Equilibrium • Center of Gravity • Newton’s Second law for torques and forces

8. Simple Machines II

9. Simple Machine = Gears and Belts • Gears are machines that transfer rotational motion • Gear/belt system linear velocity is equal Trade radius for rot. speed

10. Gear Ratio • Gears with Teeth • Belts or Smooth disks

11. Gears/Belts: What are they good for? • Transfer rotational motion • Adjust the direction of motion • Change the torque….

12. Torque and Power • Torque (rotational equivalent of force) changes with radius • Power depends on both torque and rotational speed

13. Example Question: Bicycle • A bike is set such that it has 44 teeth on the front gear and 11 teeth on the rear gear • What is the use of this setting? • Then in a “Granny” setting it has 15 teeth on the front gear and 30 teeth on the rear gear • What is the use of this setting? Going downhill or fast! Going uphill!

14. Example Question: Gears • Which way does Gear C turn? • What is the ang. velocity of Gear C in rev/min?

15. Simple Machine: Lever • Lever is a machine that improves mechanical advantage by using rotation • In a lever the applied force can be reduced by increasing the distance between force and fulcrum Increasing r allows for decreasing F

16. Example Question: Lifting students • If the fulcrum is placed in the middle it takes me 1 kN of force to lift two students. Now, if I place the fulcrum such that it is ¾ of the way from my end, how much force do I need? A third of the force!

17. Three kinds of levers: Video • http://www.youtube.com/watch?v=PW7ztbwJKBk • This movie reminds me of a high school film strip, but is useful…

18. Static Equilibrium • Forces should not cause linear acceleration • Torques should not cause rotational acceleration • Object has no rotational or linear motion

19. Example: Wheelbarrow • I want to use a wheelbarrow to move 30 kg of yard waste with a center of mass 0.2 m from the wheel axle. If the handle is located at 1 m from the wheel axle how much force should I use to keep the wheelbarrow lifted? • What is my mechanical advantage? F=(30kg)(9.8 m/s^2)(0.2 m)/(1 m) = 60 N MA=(30kg)(9.8 m/s^2)/(60 N) = 5

20. Main Points • Gears transfer rotational motion, as the radius of the gear increases there is more torque for the same amount of force • Levers use torque to lift a load, as the length of the lever arm increases the force needed decreases • Static Equilibrium – both forces and torques on an object have to sum to zero