advertisement

-Angular and Linear Quantities -Rotational Kinetic Energy -Moment of Inertia AP Physics C Mrs. Coyle Tangential (Linear) Speed and Angular Speed s=qr v ds dt r dq r dt v r Tangential Acceleration and Angular Acceleration at dv dt r d r dt a r Angular and Linear Quantities • Displacements • Speeds • Accelerations s qr v r a r • 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 aC v 2 r r v is the tangential speed 2 Resultant Linear Acceleration • The net acceleration is the sum of the tangential and centripetal accelerations. a a a 2 r 2 t Rotational Kinetic Energy • A particle in a rotating object has rotational kinetic energy: Ki = ½ mivi2 , vi = i r (tangential velocity) For the Object: KR K i KR i 1 2m r i i 2 2 i 1 1 2 2 2 m i ri I 2 i 2 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 1 2 2 K R K i m i ri i i 2 KR 1 1 2 2 2 m i ri I 2 i 2 • 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 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