-Angular and Linear Quantities -Rotational Kinetic Energy -Moment of Inertia

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

2. Tangential (Linear) Speed and Angular Speed s=qr

3. Tangential Acceleration and Angular Acceleration

4. 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. Angular and Linear Quantities

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:Ki = ½ mivi2 , vi = wi 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 ω2 and b) the tangential speed of each particle and the total kinetic energy evaluated from ½ mi vi 2 Ans: a)92kg m2 , 184J , b) 6m/s,4m/s,8m/s,184J