15. Rotational Equilibrium

In a hexagonal unit cell, which of the following sets of indices correctly represents the direction from the origin to the point with coordinates $1,1,0$ in the four-index Miller-Bravais notation?

A system consists of two blocks of masses $m_1$ and $m_2$ connected by a light string over a frictionless pulley. If the system is in equilibrium, which of the following must be true about the relationship between $m_1$ and $m_2$?

A uniform stationary ladder of length $l$ leans against a smooth vertical wall, making an angle $\theta$ with the ground. If the coefficient of static friction between the ladder and the ground is $\mu$, which of the following expressions gives the minimum value of $\mu$ required to prevent the ladder from slipping?

Which of the following conditions must be satisfied for a system to be in rotational equilibrium?

A uniform beam of length $L$ and mass $M$ rests horizontally on two supports, one at the left end and one a distance $d$ from the right end. If a person of mass $m$ walks toward the right end, how close can the person get to the right end of the beam before the beam begins to tip over the right support?

A 20 kg, 5 m-long bar of uniform mass distribution is attached to the ceiling by a light string, as shown. Because the string is off-center (2 m from the right edge), the bar does not hang horizontally. To fix this, you place a small object on the right edge of the bar. What mass should this object have, to cause the bar to balance horizontally?

Two kids (m,_LEFT = 50 kg, m,_RIGHT = 40 kg) sit on the very ends of a 5 m-long, 30 kg seesaw. How far from the left end of the seesaw should the fulcrum be placed so the system is at equilibrium? (Remember the weight of the seesaw!)

In the context of equilibrium with multiple objects, what does it mean for a system to be in a state of rotational equilibrium?