A triangular rod of length L and mass M has a nonuniform linear mass density given by the equation λ=γx2, where γ=3M/(L3) and x is the distance from point P at the left end of the rod. The rod is released from rest in the position shown, and the rod begins to rotate about a horizontal axis perpendicular to the page and through point P. (d) On the axes below, sketch graphs of the magnitude of the net torque τ on the rod and the angular speed ω of the rod as functions of time tt from the time the rod is released until the time its center of mass reaches its lowest point.

A triangular rod of length L and mass M has a nonuniform linear mass density given by the equation λ=γx2, where γ=3M/(L3) and x is the distance from point P at the left end of the rod. The rod is released from rest in the position shown, and the rod begins to rotate about a horizontal axis perpendicular to the page and through point P. (d) On the axes below, sketch graphs of the magnitude of the net torque τ on the rod and the angular speed ω of the rod as functions of time tt from the time the rod is released until the time its center of mass reaches its lowest point.

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Question

A triangular rod of length L and mass M has a nonuniform linear mass density given by the equation λ=γx², where γ=3M/(L³) and x is the distance from point P at the left end of the rod.

The rod is released from rest in the position shown, and the rod begins to rotate about a horizontal axis perpendicular to the page and through point P.

(d) On the axes below, sketch graphs of the magnitude of the net torque τ on the rod and the angular speed ω of the rod as functions of time tt from the time the rod is released until the time its center of mass reaches its lowest point.

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