A system of particles on which there is no net force undergoes unconstrained rotation about the center of mass : The gravitational torque on a body can be found by treating the body as a particle with all the mass M concentrated at the center of mass. x cm 5 1 M 3 x dm y cm 5 1 M 3 y dm SUMMARY The goal of Chapter 12 has been to understand the physics of rotating objects. General Principles Rotational Dynamics Every point on a rigid body rotating about a fixed axis has the same angular velocity and angular acceleration Newton’s second law for rotational motion is Use rotational kinematics to find angles and angular velocities. a5 t net I a . v Conservation Laws Energy is conserved for an isolated system. • Pure rotation • Rolling Angular momentum is conserved if • Particle • Rigid body rotating about axis of symmetry L r 5 I v r L r 5 r r 3 p r t r net 50 r . E 5 K rot 1 K cm 1 U g 5 1 2 I v 2 1 1 2 Mv cm 2 1 Mgy cm E 5 K rot 1 U g 5 1 2 I v 2 1 Mgy cm Important Concepts
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