A net $\tau$ applied to an object causes which of the following?

A uniform beam of length $L$ and mass $m$ is pivoted at one end and held horizontally by a force $F$ applied upward at the other end. What is the net torque about the pivot (axle) if the beam is in equilibrium?

A uniform bar of length $L$ and mass $m$ is pivoted at one end (indicated by a dot) and held horizontally. A force $F$ is applied vertically upward at the free end. What is the net torque about the pivot point?

A uniform pole of length $L$ is hinged at point A and held in equilibrium by a horizontal rope attached to its free end. If the tension in the rope is $T$, what is the magnitude of the torque $\tau$ on the pole about point A due to the tension in the rope?

Which of the following best describes the shear force diagram for a simply supported beam subjected to a single downward point load at its center, following the standard sign convention ($V$ positive shear causes clockwise rotation of the left segment)?

Which of the following best describes the shape of the bending moment diagram for a simply supported beam subjected to a uniformly distributed load along its entire length, following the standard sign convention ($\mathrm{positive} \mathrm{moment} \mathrm{causes} \mathrm{compression} \mathrm{at} \mathrm{the} \mathrm{top} \mathrm{of} \mathrm{the} \mathrm{beam}$)?

A cantilevered beam of length $L$ is fixed at end A and free at end B. If a downward point load $P$ is applied at the free end B, what is the slope at end A of the beam? (Assume the beam has constant flexural rigidity $EI$.)

Given a rigid body in equilibrium resting on a surface, what is the expression for $\tau n_{}$, the torque about point P due to the normal force $N$ applied at a distance $r$ from point P?