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8-13Q

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Physics Principles with Applications
Found in: Page 198
Physics Principles with Applications

Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

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Illustration

Short Answer

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

FIGURE 8-34 Question 13.

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

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

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.

Most popular questions for Physics Textbooks

In what direction is the Earth’s angular velocity vector as it rotates daily about its axis, north or south?

Two wheels having the same radius and mass rotate at the same angular velocity (Fig. 8–38). One wheel is made with spokes so nearly all the mass is at the rim. The other is a solid disk. How do their rotational kinetic energies compare?

(a) They are nearly the same.

(b) The wheel with spokes has about twice the KE.

(c) The wheel with spokes has higher KE, but not twice as high.

(d) The solid wheel has about twice the KE.

(e) The solid wheel has higher KE, but not twice as high.

FIGURE 8-38

MisConceptual Question 7.

Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.

If there were a great migration of people toward the Earth's equator, the length of the day would

(a) increase because of conservation of angular momentum.

(b) decrease because of conservation of angular momentum.

(c) decrease because of conservation of energy.

(d) increase because of conservation of energy.

(e) remain unaffected.

The moment of inertia of a rotating solid disk about an axis through its CM is \(\frac{{\bf{1}}}{{\bf{2}}}{\bf{M}}{{\bf{R}}^{\bf{2}}}\) (Fig. 8–20c). Suppose instead that a parallel axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller? Explain why.
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