Lecture 20 Rigid Body An extended object in which the distance between any two point in the object is constant in time Effect of external forces on a rigid body they translate and rotate Rotational motion about the center of mass Torque about center of mass produces angular acceleration about the center of mass is the moment of inertia about the center of mass is the angular acceleration about the center of mass Magnitude of torque 1 Force F exerted on a point P on a rigid body 2 Vector r from center of mass located at point S to point P 3 Extended the line from S to P Denote the angle between the extended line and the force by theta Magnitude of torque about point S due to the force exerted at point P Torque Diagram 1 Draw all external forces at the point where they are acting 2 Identify the point S where we are calculating the torque 3 Draw r for each force Draw a curved arrow from r to F tail to tail and use right hand rule The way your thumb is pointing is the direction of torque How can vectors A and B de ne a new vector C up to a direction a magnitude of c b direction of c Vector Product of Unit Vectors Unit vectors in cylindrical coordinate Torque due to uniform gravitational force Z Component of Torque about point S Only consider tangential force Vector from S to point of action of force at P z component of torque about S Tangential force on mass element produces z component of torque The total torque on a rigid body due to the gravitational force can be determined by placing all of the gravitational force at the center of mass of the object
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