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 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?

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?

Suppose that you can lift no more than 650 N (around 150 lb) unaided.

(a) How much can you lift using a 1.4-m-long wheelbarrow that weighs 80.0 N and whose center of gravity is 0.50 m from the center of the wheel (Fig. E11.16)? The cen-ter of gravity of the load car-ried in the wheelbarrow is also 0.50 m from the center of the wheel. (b) Where does the force come from to enable you to lift more than 650 N using the wheelbarrow?

Suppose that you can lift no more than 650 N (around 150 lb) unaided.

How much can you lift using a 1.4 m-long wheelbarrow that weighs 80.0 N and whose center of gravity is 0.50 m from the center of the wheel (Fig. E11.16)? The center of gravity of the load carried in the wheelbarrow is also 0.50 m from the center of the wheel.

A uniform 300-N trapdoor in a floor is hinged at one side. Find the net upward force needed to begin to open it and the total force exerted on the door by the hinges if the upward force is applied at the center of the edge opposite the hinges.