15. Rotational Equilibrium

A rectangular current loop of width $w$ and height $h$ carries a current $I$ and is placed in a uniform magnetic field $B$ such that the plane of the loop makes an angle $\theta$ with the magnetic field. What is the magnitude of the torque acting on the loop?

A pipe assembly is subjected to an $80-N$ force applied at a point $A$. If the position vector from point $B$ to point $A$ is $r=3i+4j$ meters, and the force vector is $F=80j$ newtons, what is the moment of this force about point $B$?

When you open a laptop that is facing you by lifting the screen upward, what is the direction of the applied $\tau$ (torque) relative to the laptop's hinge axis?

A uniform seesaw is balanced on a fulcrum at its center. A child of mass $m$ sits at a distance $d$ to the right of the fulcrum, and another child of mass $2m$ sits at a distance $\frac{1}{2}d$ to the left of the fulcrum. In what direction will the seesaw rotate, and what will be the sign of the angular acceleration $\alpha$ (taking counterclockwise as positive)?

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 $EI$.)

A uniform board is pivoted at one end. Four forces of equal magnitude are applied at different points and angles: Force $A$ is applied perpendicular to the board at its far end, Force $B$ is applied at the midpoint at a $45°$ angle to the board, Force $C$ is applied parallel to the board at its far end, and Force $D$ is applied perpendicular to the board at its midpoint. Which force exerts the largest magnitude torque on the board?

Given a force $F$ applied by the Achilles' tendon at a perpendicular distance $r$ from point P, what is the torque ${\tau }_f$ about point P due to this force?

In a system that is in rotational equilibrium, how do the clockwise and counterclockwise $\tau$ compare?

A seesaw is balanced on a fulcrum at its center. A child of mass $m$ sits at a distance $d$ to the left of the fulcrum, and another child of mass $2m$ sits at a distance $\frac{1}{2}d$ to the right of the fulcrum. In what direction will the seesaw rotate, and what will be the sign of the angular acceleration $\alpha$ (alpha) about the fulcrum?

A uniform box of mass $m$ and length $L$ rests on a horizontal table, with one end of the box extending beyond the edge. How far can the center of the box be from the end of the table before the box begins to tip over?

In problems involving $\tau$ (torque) and rotational equilibrium, why are clockwise moments typically assigned a negative sign when summed with counterclockwise moments?

If the net $\tau$ on an object adds up to $0$, which of the following must be true about the object?

A uniform horizontal beam of length $L$ and mass $m$ is bolted to a wall at one end and extends outward. If a force $F$ is applied vertically upward at the free end of the beam, what is the magnitude of the torque about the point where the beam is bolted into place due to this force?

A seesaw is balanced on a fulcrum at its center. Child A with mass $m{A}_1$ sits at a distance $d{A}_1$ to the left of the fulcrum, and Child B with mass $m{B}_2$ sits at a distance $d{B}_2$ to the right. If $m{A}_1\times d{A}_1>m{B}_2\times d{B}_2$, in what direction will the seesaw rotate?

A pulley of radius $R$ has a rope wrapped around it with a tension $T$ acting tangentially. What is the net torque about the axle on the pulley?