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

2. Convert 14.0 rotations to radians:
Angle Conversions:
1 rev = 1 rot = 2π rad = 360 deg
Convert 14.0 rotations to radians:
88.0 rad

3. Convert 120. radians to rotations:
Angle Conversions:
1 rev = 1 rot = 2π rad = 360 deg
Convert 120. radians to rotations:
19.1 rot

4. Convert 170. degrees to radians:
Angle Conversions:
1 rev = 1 rot = 2π rad = 360 deg
Convert 170. degrees to radians:
2.97 rad

5. Convert 1.5708 radians into degrees:
Angle Conversions:
1 rev = 1 rot = 2π rad = 360 deg
Convert radians into degrees:
90.0 degrees

6.  = Δθ/t (omega is in rad/s, rot/s, and RPM)
Angular velocity:
 = Δθ/t (omega is in rad/s, rot/s, and RPM)
1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
RPM = rev/min

7. Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
Convert 15.0 rot/s to rad/s:
94.2 rad/s

8. Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
Convert 67.0 rad/s to rot/s:
10.7 rot/s

9. Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
Convert 78.0 RPM to rad/s:
8.17 rad/s

10. Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
Convert 12.2 rad/s to RPM:
117 RPM

11. Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
Convert 3.20 rot/s to RPM
192 RPM

12. Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg
1 minute = 60 seconds
Convert 45 RPM to rot/s
0.750 rot/s

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

14. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A 68.0 cm diameter car tire rolls through 16.0 radians. What distance does the car travel?
5.44 m

15. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A 41.0 cm radius bike tire rolls 50.0 m. Through what angle in radians does the tire rotate?
122 radians

16. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A m radius tire is rotating at 230. rad/s. What is the lineal speed at the edge of the wheel?
73.6 m/s

17. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A 1.60 m diameter aircraft landing wheel strikes the ground at 54.0 m/s. What is the angular velocity of the wheel?
67.5 rad/s

18. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A skateboard with 52.0 mm wheels that are accelerating angularly at 120. rad/s/s has what linear acceleration?
(52.0 mm is the diameter)
3.12 m/s/s

19. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A skateboard with 64.0 mm (diameter) wheels accelerates at 4.50 m/s/s. What is the angular acceleration of the skateboard?
141 rad/s/s

21. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A 78.0 cm diameter wheel rolls through 23.0 rotations. What lineal distance does it travel?
56.4 m

22. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A skateboard with 64.0 mm (diameter) rolls 100. m. Through how many rotations do the wheels rotate?
497 rotations

23. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A m radius grinding wheel rotates at 750. RPM. What is the lineal speed at its edge?
26.7 m/s

24. s = θr, v = r, a = r Tangential Relationships:
r is radius in m, and you must be in radians!!!!!
A pitching machine uses 1.20 m diameter rotating wheels. What is their speed in RPM if it is pitching at 41.0 m/s?
653 RPM