1. -Angular and Linear Quantities -Rotational Kinetic Energy -Moment of Inertia AP Physics C Mrs. Coyle

2. Tangential (Linear) Speed and Angular Speed s=  r 

3. Tangential Acceleration and Angular Acceleration

4. Angular and Linear Quantities Displacements Speeds Accelerations Every point on the rotating object has the same angular motion but not the same linear motion. The a and v are functions of r.

5. Remember: Centripetal Acceleration v is the tangential speed

6. Resultant Linear Acceleration The net acceleration is the sum of the tangential and centripetal accelerations.

7. Rotational Kinetic Energy A particle in a rotating object has rotational kinetic energy: K i = ½ m i v i 2, v i =  i r (tangential velocity) For the Object:

8. Rotational Kinetic Energy and Moment of Inertia The total rotational kinetic energy of the rigid object is the sum of the energies of all its particles I is called the moment of inertia

9. Moment of Inertia, I Moment of Inertia, I, is a measure of the resistance of an object to changes in its rotational motion. Moment of Inertia is analogous to mass in translational motion.

10. Example #20 Rigid rods of negligible mass lying along the y axis connect three particles. If the system rotates about the x-axis with an angular speed of 2.00rad/s find a) the moment of inertia about the x-axis and the total rotational kinetic energy evaluated from ½ I ω 2 and b) the tangential speed of each particle and the total kinetic energy evaluated from ½ m i v i 2 Ans: a)92kg m 2, 184J, b) 6m/s,4m/s,8m/s,184J