15. Rotational Equilibrium

Which three factors determine the magnitude of the $\tau$ (torque) produced by a $F$ (force) about a specific pivot point?

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)?

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

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 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 uniform bar of length $L$ is pivoted at one end and held horizontally. A force $F$ is applied vertically upward at the free end. What is the net torque about the pivot due to the force $F$?

A pulley of radius $R$ has two forces applied tangentially at its rim: a force $F$ clockwise and a force $2F$ counterclockwise. What is the net torque on the pulley about the axle?

A composite disc is made out of two concentric cylinders, as shown. The inner cylinder has radius 30 cm. The outer cylinder has radius 50 cm. If you pull on a light rope attached to the edge of the outer cylinder (shown left) with 100 N, how hard must you pull on a light rope attached to the edge of the inner cylinder (shown right) so the disc does not spin?

A uniform seesaw of length $4.0m$ is balanced on a pivot at its center. A child of mass $30\mathrm{kg}$ sits $1.5m$ to the right of the pivot. How far to the left of the pivot must a $4.0\mathrm{kg}$ cat stand to keep the seesaw balanced (neglecting the mass of the seesaw)?

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?

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?