Chapter 8, Problem 16Q

To determine

The reason why the tightrope walkerscarry a long narrow rod.

Answer to Problem 16Q

Solution:

When a tightrope walker walks on a tightrope, earth’s gravity exerts a fixed torque on him. By increasing the length, the walker increases I , in turn decreasing the value of a . This helps in steadying him as he walks along the rope.

Explanation of Solution

The moment of inertia of a long, narrow road is given by:

  $I=\frac{1}{12}m{l}^2$

Where, m is the mass of the rod and l is the length of the rod

Therefore, greater the length of a rod, higher is the moment of inertia

Torque, $\tau =I\times \alpha$ , where a is angular acceleration

This gives, $\alpha =\tau /I$

i.e. for the same torque, higher the value of I , lower is the angular acceleration

Conclusion:

Thus, the tightrope walkers carry a long narrow rod because this helps in steadying him as he walks along the rope.