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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 A B τ τ < 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 τ = 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 τ τ = In conclusion, 0 D B A C τ τ τ

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