2. Angular Mechanics - Radians r  s Full circle: 360 o = 2  Radians  = s/r Radians = m/m = ? TOC

3. Angular Mechanics - Angular Quantities Linear: (m) s (m/s) u (m/s) v (m/s/s) a (s) t Angular:  - - o-o- -- -- t-t- TOC

4. Conversions TOC Radians Revolutions Rad/s Rev/min (RPM) = = = = =

5. How many radians in 3.16 revolutions? 19.9 rad W

6. If a drill goes through 174 radians, how many revolutions does it go through? 27.7 rev W

7. Convert 33 RPM to rad/s 3.5 rad/s W

8. Convert 12 rev/s to rad/s 75 rad/s W

9. Angular Mechanics - Tangential Relationships Linear: (m) s (m/s) v (m/s/s) a Tangential: (at the edge of the wheel) =  r - =  r - =  r - TOC *Not in data packet

10. Example: s =  r, v =  r, a =  r A certain gyro spinner has an angular velocity of 10,000 RPM, and a diameter of 1.1 cm. What is the tangential velocity at its edge? TOC

11. What is the tangential velocity of a 13 cm diameter grinding wheel spinning at 135 rad/s? 8.8 m/s W

12. What is the angular velocity of a 57 cm diameter car tire rolling at 27 m/s? 95 rad/s W

13. A.450 m radius marking wheel rolls a distance of 123.2 m. What angle does the wheel rotate through? 274 rad W

14. A car with.36 m radius tires speeds up from 0 to 27 m/s in 9.0 seconds. (a) What is the linear acceleration? 3.0 m/s/s W

15. A car with.36 m radius tires speeds up from 0 to 27 m/s in 9.0 seconds. (a) a = 3.0 m/s/s (b) What is the tire’s angular acceleration? a =  r 8.3 Rad/s/s W

16. A car with.36 m radius tires speeds up from 0 to 27 m/s in 9.0 seconds. (a) a = 3.0 m/s/s (b)  = 8.3 Rad/s/s (8.33333333) (c) What angle do the tires go through? s =  r, s = (u + v)t/2, 340 Rad W

17. Angular Mechanics - Angular kinematics Linear:  s/  t = v  v/  t = a u + at = v ut + 1 / 2 at 2 = s u 2 + 2as = v 2 (u + v)t/2 = s *Not in data packet TOC

18. Example: My gyro spinner speeds up to 10,000 RPM, in.78 sec. What is its angular accel., and what angle does it go through? TOC

19. Use the formula  =  /  t to convert the angular velocity 78 RPM to rad/s. Hint: t = 60 sec,  = 78(2  ) 8.2 rad/s W

20. A turbine speeds up from 34 rad/s to 89 rad/s in 2.5 seconds. What is the angular acceleration? 22 rad/s/s W

21. A turbine speeds up from 34 rad/s to 89 rad/s in 2.5 seconds. What is the angular acceleration? (b) What angle does it go through? 150 rad W

22. A wheel stops from 120 rad/s in 3.0 revolutions. (a) What is the angular acceleration? -380 rad/s/s W

23. A wheel stops from 120 rad/s in 3.0 revolutions. (a) What is the angular acceleration? (b) What time did it take?  = 381.97 = -380 rad/s/s.31 s W

24. A motor going 45.0 rad/s has an angular acceleration of 12.4 rad/s/s for 3.7 seconds. (a) What is the final velocity? 91 rad/s W

25. A motor going 45.0 rad/s has an angular acceleration of 12.4 rad/s/s for 3.7 seconds. (a) What is the final velocity? (b) What angle does it go through?  =  o t + 1 / 2  t 2 250 rad W

26. Angular Mechanics - Tangential Relationships Linear: (m) s (m/s) v (m/s/s) a Tangential: (at the edge of the wheel) =  r - =  r - =  r - Acceleration* - tangential TOC *Not in data packet

27. Angular Mechanics – Tangential and radial TOC Radial r = -Centripetal

28. Angular Mechanics – Centripetal Acceleration TOC a = v 2 /r v =  r a = v 2 /r = (  r) 2 /r a =

29. Example: What’s the centripetal acceleration 5.0 cm from the axis of a 10,000 RPM centrifuge? TOC

30. What is the centripetal acceleration of a point 35 cm from an axis of a wheel that has an angular velocity of 12 rad/s? 50. m/s/s W

31. A car has 68 cm diameter wheels, and is going at a constant speed of 32 m/s. What is the tangential acceleration, and what is the radial acceleration? (centrip) 3.0E3 m/s/s W

32. What is the angular velocity of a centrifuge if it pulls 2000. “g”s with a radius of 6.7 cm? How many RPMs is this? 540 rad/s 5200 RPM W