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

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

Tangential Acceleration and Angular Acceleration

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.

Remember: Centripetal Acceleration v is the tangential speed

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

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:

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

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.

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