1. Rotational Motion Phys 114 Eyres

2. Circles: Remember T is time to go around once

3. Rotational kinematics © 2014 Pearson Education, Inc.

4. Rotational kinematics © 2014 Pearson Education, Inc.

5. Rotational (angular) position  © 2014 Pearson Education, Inc.

6. Quantities and Units Angular Position:  (radians or degrees) Angular Velocity:  (radians/sec) Angular Acceleration:  (rad/sec^2)

7. Rotational (angular) velocity ω © 2014 Pearson Education, Inc.

8. Rotational (angular) acceleration α © 2014 Pearson Education, Inc.

9. Rotating Tire A tire placed on a balancing machine in a service station starts from rest and turns through 4.7 revolutions in 1.2 s before reaching its final angular speed. Calculate its angular acceleration. t =  =  = t =  =  =  = =

10. Rotating Tire A tire placed on a balancing machine in a service station starts from rest and turns through 4.7 revolutions in 1.2 s before reaching its final angular speed. Calculate its angular acceleration. t =0  =0  =0 t =1.2 s  =4.7 revs  =  = =

11. Rotating Tire t =0  =0  =0 t =1.2 s  =29.53 rads  =49.2 rad/s

12. Circular or Angular? Velocity Acceleration: What are the clues?

13. Tangential and Angular Tangential Relating equation Think of C=(2π)r Angular Arc length, s (m) Tangential velocity, v t (m/s) Tangential accel., a t (m/s 2 ) Radial Quantity relating to tangential or angular Radial Acceleration, a r (m/s 2 )

14. Relating translational and rotational quantities and tip © 2014 Pearson Education, Inc.

15. The unit for rotational position is the radian (rad). It is defined in terms of: – The arc length s – The radius r of the circle The angle in units of radians is the ratio of s and r: The radian unit has no dimensions; it is the ratio of two lengths. The unit rad is just a reminder that we are using radians for angles. Units of rotational position © 2014 Pearson Education, Inc.

16. Rotating Tire A tire placed on a balancing machine in a service station starts from rest and turns through 4.7 revolutions in 1.2 s before reaching its final angular speed. Calculate the tangential quantities when r=0.4 m: Final tangential velocity Tangential displacement Average tangential acceleration Radial acceleration t =0  =0  =0 t =1.2 s  = 29.53 rads  =49.2 rad/s t =1.2 s s = v = t =0 s =0 v =0 a t =

17. Rotating Tire t =0  =0  =0 t =1.2 s  = 29.53 rads  =49.2 rad/s t =1.2 s s = v = t =0 s =0 v =0 a t =

18. Rotating Tire t =0  =0  =0 t =1.2 s  =4.7 revs  =49.2 rad/s t =1.2 s s =11.81 m v =19.7 m/s t =0 s =0 v =0 a t =

19. Rotating Tire t =0  =0  =0 t =1.2 s  =4.7 revs  =49.2 rad/s t =1.2 s s =11.81 m v =19.7 m/s t =0 s =0 v =0 a t = 16.4 m/s 2 Solve for radial acceleration: How do you decide what velocity to use in solving?

20. Tangential and Angular LinearAngular There is an angular equivalent for almost everything that you have learned.

21. Bug (a)What is the tangential acceleration of a bug on the rim of a 10-in.-diameter disk if the disk moves from rest to an angular speed of 78 rev/min in 3.0 s? (b) When the disk is at its final speed, what is the tangential velocity of the bug? (c) One second after the bug starts from rest, what are its tangential acceleration, centripetal acceleration, and total acceleration?

22. Answers Bug: a) tan accel = 0.35 m/s 2 b) 1.0 m/s c) 0.35 m/s 2, 0.95 m/s 2, 1.0 m/s 2 at 20  forward from radial axis