9.4. Newton’s Second Law for Rotational Motion A model airplane on a guideline has a mass m and is flying on a circle of radius r (top view). A net tangential.

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Presentation transcript:

9.4. Newton’s Second Law for Rotational Motion A model airplane on a guideline has a mass m and is flying on a circle of radius r (top view). A net tangential force F T acts on the plane.

NEWTON’S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS

Moment of Inertia of point masses

Moment of Inertia, I for Extended regular- shaped objects

9.5 Rotational Work and Energy Work and energy are among the most fundamental and useful concepts in physics. The force F does work in rotating the wheel through the angle .

ROTATIONAL WORK The rotational work W R done by a constant torque  in turning an object through an angle  is SI Unit of Rotational Work: joule (J)

ROTATIONAL KINETIC ENERGY

Demo on Rolling Cylinders

9.6 Angular Momentum The angular momentum L of a body rotating about a fixed axis is the product of the body's moment of inertia I and its angular velocity  with respect to that axis: SI Unit of Angular Momentum: kg · m 2 /s.

CONSERVATION OF ANGULAR MOMENTUM The total angular momentum of a system remains constant (is conserved) if the net external torque acting on the system is zero.

Demonstration on Conservation of angular momentum

Problem A woman stands at the center of a platform. The woman and the platform rotate with an angular speed of 5.00 rad/s. Friction is negligible. Her arms are outstretched, and she is holding a dumbbell in each hand. In this position the total moment of inertia of the rotating system (platform, woman, and dumbbells) is 5.40 kg·m 2. By pulling in her arms, she reduces the moment of inertia to 3.80 kg·m 2. Find her new angular speed.