1. Chapter 8
Rotational Motion

2. Why rotational? We’ve focused on translational motion up to this point
Rotational motion has things in common with translational motion
Examples: spinning wheels,
washing machine drum,
merry-go-round, etc.

3. Angular Quantities
Quantities in linear motion have a corresponding quantity in rotational motion

4. Angular Position
Angular displacement is the angle (in rads) through which a point or line has been rotated about an axis

5. The rate of change of angular displacement ΔӨ with time Δt
Angular Velocity
The rate of change of angular displacement ΔӨ with time Δt

6. Instantaneous Angular Velocity

7. Instantaneous Acceleration
Angular Acceleration
The rate of change of angular velocity
Instantaneous Acceleration

8. Period
The time it takes to complete one cycle or revolution. Also the reciprocal of the frequency.
T=1 f

9. Look familiar?!
The equations of motion for constant angular acceleration are the same as those for linear motion, with the substitution of the angular quantities for the linear ones.

10. Torque
From experience, we know that the same force will be much more effective at rotating an object such as a nut or a door if our hand is not too close to the axis.
This is why we have long-handled wrenches, and why doorknobs are not next to hinges.

11. Torque To make an object start rotating, a force is needed
A longer lever arm is very helpful in rotating objects.

12. The length of the lever arm r┴
Torque depends on
The length of the lever arm r┴
The force applied F
Torque is calculated

13. Only the tangential component of force causes a torque

14. Moment of Inertia The rotational equivalent of mass
Symbolized with letter I

15. Angular Momentum
Angular momentum-the product of the angular velocity of a body and its moment of inertia about the axis of rotation. Depends on the mass of the object and how it is distributed

16. Rotational Kinetic Energy
We have learned that the kinetic energy of an object is
By substituting the rotational quantities, we find that the rotational kinetic energy is:
An object that has both translational and rotational motion must take both into account to find the total KE

17. Rotational Kinetic Energy
Torque does work as it moves the wheel through an angle θ:

18. The work-energy theorem still applies!
A torque acting through an angular displacement does work, just as a force acting through a distance does.
The work-energy theorem still applies!

19. Vector Nature of Angular Quantities
We have considered the magnitude of the angular quantities but must also define the direction!
The angular velocity vector points along the axis of rotation; its direction is found using a right hand rule:
Curl fingers around the axis in the direction of rotation
Thumb is pointing in direction of ω

20. Vector Nature of Angular Quantities
Angular acceleration and angular momentum vectors also point along the axis of rotation.

22. References
Giancoli, Douglas. Physics: Principles with Applications 6th Edition
Walker, James. AP Physics: 4th Edition. 2010
Zitewitz. Physics: Principles and Problems. 2004