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Transcript
Newton’s 2nd Law for Rotation, Angular Momentum, Rotational Kinetic Energy Rotation Physics Mr. McCallister Newton’s 2nd Law for Rotation • Recall Newton’s Second Law: –F=ma – Force = mass x acceleration • Newton’s Second Law for Rotation states: –τ=Iα – torque = moment of inertia x angular acceleration Practice 8C, #2-3 • #1 – Worked on board • Due NEXT Tuesday, 2-16-10 Angular Momentum • Recall linear (or translational) momentum: –p=mv – momentum = mass x velocity • Angular momentum is “the product of a rotating object’s moment of inertia and angular speed about the same axis – Symbol: L , Unit: kg m2 / s –L=Iω – angular momentum = moment of inertia x angular speed Conservation of Angular Momentum • If no net torque is acting on a system, then the system’s angular momentum will be conserved • Example: figure skater’s spin – Decreasing I will yield increased ω to conserve L. Practice 8D, #2-5 • #1 – Worked on board • Due NEXT Tuesday 2-16-10 Rotational Kinetic Energy • Recall linear (or translational) kinetic energy – KEtrans = ½ m v2 • Rotational kinetic energy is due to an object’s rotational motion – KErot = ½ I ω2 – rotational kinetic energy = ½ x moment of inertia x (angular speed)2 Conservation of Mechanical Energy • If only conservative forces (i.e. gravitational, normal) are acting on a system, the system will conserve mechanical energy • However, now ME = KEtrans + KErot + PEg – ME = ½ m v2 + ½ I ω2 + m g h Practice 8E #2,3 and Section Review • Sample Problem 8E – worked on board • Due NEXT Tuesday, 2-16-2010