Recitation Worksheet N Solutions

Recitation Worksheet N Solutions - Worksheet N: Rigid body...

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Worksheet N: Rigid body motion (II) 1. Several forces F are applied to the 2D objects below. All forces have equal magnitude. All the objects have the same mass, uniformly distributed. . Rank the net torque about the center of mass for each of the objects. Drawn in red are the lever-arm vectors r for each of the forces for rotations about the center of mass. In case A, the torque is simply 2 A d F τ = . In case B, it’s a little larger, because of the additional force (note that the new torque is less than Fd/2 because r and F are not perpendicular). So AB < In case C, the vertical force is applied on the center of mass, and thus r = 0; the horizontal force is parallel to the corresponding r and thus r×F = 0. Thus 0 C = In case D, the force that is directed toward the center of the disk is antiparallel to the corresponding r, thus r×F = 0. The other two forces produce exactly the same torque as in case B (assuming that the angle is the same, as suggested by the figure). Thus D B = In conclusion, 0 DBAC τττ =>>= d d d d /2 [A] [B] [C] [D] r
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Recitation Worksheet N Solutions - Worksheet N: Rigid body...

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