Question

in the picture below, a bar is set up to rotate about its center (the dark circle). each arrow represents a force that is being applied to the bar. each force has the same
center as the pivot point, answer the following questions.
a.) which force has no lever arm?

b.) which force will create the most torque?

Explanation:

Step1: Recall the formula for torque

Torque $\tau = rF\sin\theta$, where $r$ is the lever - arm (distance from the pivot point to the line of action of the force), $F$ is the force magnitude, and $\theta$ is the angle between the force vector and the position vector from the pivot to the point of application of the force.

Step2: Analyze the lever - arm for each force

• For force $A$: The line of action of force $A$ passes through the pivot point. So, $r = 0$. Using the torque formula $\tau = rF\sin\theta$, when $r = 0$, $\tau=0$.
• For force $B$: The force is perpendicular to the bar, and $r

eq0$.

• For force $C$: The force is perpendicular to the bar, and $r

eq0$.

• For force $D$: The force is perpendicular to the bar (assuming the bar is horizontal and the force is vertical), and $r

eq0$.

Step3: Compare the magnitudes of the lever - arms for torque calculation

Since $\tau = rF\sin\theta$ and $F$ is the same for all forces (given) and $\sin\theta = 1$ (assuming all non - zero lever - arm forces are perpendicular to the bar), the force with the largest $r$ will create the most torque. Force $D$ has the largest distance ($r$) from the pivot point among the non - zero lever - arm forces.

Answer:

a. $A$
b. $D$