15. Rotational Equilibrium

For a simply supported beam of length $L$ with a uniformly distributed load $w$ along its entire length, which of the following correctly describes the shape of the shear force and bending moment diagrams?

For a cantilever beam of length $L$ fixed at the left end and subjected to a downward point load $P$ at the free right end, which of the following best describes the shapes of the shear force and bending moment diagrams along the beam?

A uniform beam of length $L$ and mass $m$ rests horizontally on two supports, one at each end. If a downward force $F$ is applied at a distance $a$ from the left end, which expression gives the reaction force at the left support?

In the context of equilibrium with multiple supports, what is the name of a horizontal structure that is supported at only one end?

A uniform beam of length $L$ and mass $m$ rests horizontally on two supports, one at each end. If a point load $P$ is applied at a distance $a$ from the left end, which of the following correctly gives the reaction force at the left support?

A uniform horizontal beam of length $L$ and mass $m$ rests on two supports, one at each end. If a downward force $F$ is applied at a distance $d$ from the left end, which equation correctly expresses the condition for rotational equilibrium about the left support (taking counterclockwise moments as positive)?

A uniform beam of length $L$ and mass $m$ rests horizontally and is supported at two points, A and B, which are located at the ends of the beam. If the beam is in static equilibrium and no other forces act on it except gravity, what is the reaction force at support A?

A uniform beam of length $L$ and mass $m$ rests horizontally on two supports, one at each end. If a downward point load $P$ is applied at a distance $a$ from the left end, which of the following expressions gives the reaction force at the left support?

A board 8 m in length, 20 kg in mass, and of uniform mass distribution, is supported by two scales placed underneath it. The left scale is placed 2 m from the left end of the board, and the right scale is placed on the board's right end. A small object 10 kg in mass is placed on the left end of the board. Calculate the reading on the left scale. (Use g=10 m/s².)

BONUS:Calculate the reading on the right scale.