Question

Why do tightrope walkers (Fig. 8–34) carry a long, narrow rod?

FIGURE 8-34 Question 13.

Short answer

The long rod helps in maintaining balance while walking over the rope.

Step-by-step solution

Meaning of torque

The term "torque" may be described as the twisting force that causes revolution in a body.

Its value relies on the applied force's position, direction, and significance. It is considered a movement force.

Moment of inertia of a long rod

Let\(M\)be the mass of the rod and\(L\)be its length.

The expression for the moment of inertia of the long rod is given as:

\(I = \frac{1}{{12}}M{L^2}\) … (i)

The expression for the angular acceleration is given as:

\(\alpha = \frac{\tau }{I}\)

Substitute the value of equation (i) in the above equation.

\(\begin{aligned}{c}\alpha = \frac{\tau }{{\left( {\frac{1}{2}M{L^2}} \right)}}\\\alpha = \frac{{12\tau }}{{M{L^2}}}\end{aligned}\)

From the above-mentioned equation, it is clear that for a given value of torque, the angular acceleration produced is inversely related to the mass of the rod and the square of its length.

The longer the rod, the lesser will be the angular acceleration produced. When a tightrope walker walks over a tight rope, the gravitational force exerts a torque on her/his body, which tends to rotate her body.

If the angular acceleration is large, then she/he would lose balance easily. By holding the long rod, she/he increases the moment of inertia and thus reduces the angular acceleration.