13. Rotational Inertia & Energy

A force of magnitude $F$ acts at a distance $r$ from point O, making an angle $\theta$ with the position vector from O to the point of application. Which expression gives the moment (torque) of the force about point O?

In physics, what is the term used to describe a twisting force that causes rotation about an axis?

Suppose three bolts are tightened using wrenches of equal length, but different forces are applied at different angles: Bolt A with a force of $20$ N at $90°$, Bolt B with a force of $25$ N at $60°$, and Bolt C with a force of $30$ N at $30°$. If the length of each wrench is $0.2$ m, in which order, from greatest to least, are the torques exerted on the bolts?

When using a wrench to loosen a nut, how does the torque produced change if you decrease the distance from the point where you apply the force to the nut (i.e., shorten the lever arm), assuming the applied force remains the same?

A uniform horizontal beam is subjected to three forces: $F_1$ acts upward at the left end (point A), $F_2$ acts downward at the midpoint, and $F_3$ acts upward at the right end (point B). The beam has length $L$. Which of the following correctly gives the moment (torque) about point A due to each force, using the convention that counterclockwise moments are positive?

Three forces act on a rigid body at different points. If force $F_1$ of magnitude $10$ N acts at a distance $2$ m from point A perpendicular to the position vector, force $F_2$ of magnitude $8$ N acts at a distance $3$ m from point A at an angle of $30°$ to the position vector, and force $F_3$ of magnitude $5$ N acts at a distance $4$ m from point A parallel to the position vector, which of the following gives the correct magnitudes of the moments (torques) of each force about point A?

In a rigid body rotating about a fixed axis, if segment CD is located at a distance $r$ from the axis and is subjected to a force $F$ perpendicular to the segment, what is the internal torque in segment CD?

A uniform rod of length $L$ and mass $m$ is pivoted at one end and held horizontally in equilibrium by a pin at the pivot. What is the magnitude of the torque that the pin must exert to keep the rod from rotating?

A rigid body is pivoted at point O and is acted upon by a force $F$ at a distance $r$ from O, making an angle $\theta$ with the position vector from O. What is the magnitude of the torque $\tau$ about point O due to this force?

In the context of torque and kinematic equations, how is the strength of the torque acting on a compass needle in a magnetic field typically indicated?

A uniform pole of length $L$ and mass $m$ is hinged at point A and held in equilibrium by a rope attached to its other end, making an angle $\theta$ with the horizontal. If the tension in the rope is $T$, what is the magnitude of the torque $\tau$ about point A due to the tension in the rope?

Given six forces applied at different points and angles on a uniform beam hinged at the left end, rank the magnitudes of the torques $\tau a_{}$ to $\tau f_{}$ about the hinge from largest to smallest.

A force of magnitude $F$ acts at a point $a$ located a distance $r$ from point $p$. If the force is applied perpendicular to the position vector from $p$ to $a$, what is the magnitude and direction of the moment (torque) of the force about point $p$?

Given a force $F$ applied at point C, and the position vector from point A to point C is $\stackrel{\mathrm{AC}}{r}$, what is the correct expression for the moment (torque) about segment AB due to $F$?

Assuming a constant wind speed, which of the following changes would increase the $\tau$ applied by the wind to a wind turbine blade?