Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 16

Each of three helicopter rotor blades shown in Fig. 9-42 is \(5.20 \mathrm{~m}\) long and has a mass of \(240 \mathrm{~kg}\). The rotor is rotating at 350 rev/min. What is the rotational inertia of the rotor assembly about the axis of rotation? (Each blade can be considered a thin rod.)

Short Answer

Expert verified
The rotational inertia of the rotor assembly about the axis of rotation is \(I = 3 \times \frac{1}{3} \times 240 \mathrm{~kg} \times (5.20 \mathrm{~m})^2 = 8192 \mathrm{~kg} \cdot \mathrm{m}^2\).

Step by step solution

01

Find the Rotational Inertia of One Blade

Start off by calculating the rotational inertia of a single blade (as if it were a thin rod) using the formula \(I = \frac{1}{3} m L^2\). Substitute \(m = 240 \mathrm{~kg}\) and \(L = 5.20 \mathrm{~m}\) into the formula and solve.
02

Calculate Total Rotational Inertia

As the rotor assembly is made up of three blades, multiply the calculated rotational inertia of a single blade by three to find the total rotational inertia of the assembly.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Vectors \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\) lie in the \(x y\) plane. The angle between \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\) is \(\phi\), which is less than \(90^{\circ}\). Let \(\overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}})\). Find the magnitude of \(\overrightarrow{\mathbf{c}}\) and the angle between \(\overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\).

Two thin rods of negligible mass are rigidly attached at their ends to form a \(90^{\circ}\) angle. The rods rotate in the \(x y\) plane with the joined ends forming the pivot at the origin. A particle of mass \(75 \mathrm{~g}\) is attached to one rod a distance of \(42 \mathrm{~cm}\) from the origin, and a particle of mass \(30 \mathrm{~g}\) is attached to the other rod a distance of \(65 \mathrm{~cm}\) from the origin. ( \(a\) ) What is the rotational inertia of the assembly? \((b)\) How would the rotational inertia change if the particles were both attached to one rod at the given distances from the origin?

An automobile traveling \(78.3 \mathrm{~km} / \mathrm{h}\) has tires of \(77.0-\mathrm{cm}\) diameter. (a) What is the angular speed of the tires about the axle? (b) If the car is brought to a stop uniformly in \(28.6\) turns of the tires (no skidding), what is the angular acceleration of the wheels? (c) How far does the car advance during this braking period?

Figure \(9-54\) shows the massive shield door at a neutron test facility at Lawrence Livermore Laboratory; this is the world's heaviest hinged door. The door has a mass of \(44,000 \mathrm{~kg}\), a rotational inertia about its hinge line of \(8.7 \times 10^{4} \mathrm{~kg} \cdot \mathrm{m}^{2}\), and a width of \(2.4 \mathrm{~m}\). What steady force, applied at its outer edge at right angles to the door, can move it from rest through an angle of \(90^{\circ}\) in \(30 \mathrm{~s}\) ?

In an Atwood's machine one block has a mass of \(512 \mathrm{~g}\) and the other a mass of \(463 \mathrm{~g}\). The pulley, which is mounted in horizontal frictionless bearings, has a radius of \(4.90 \mathrm{~cm}\). When released from rest, the heavier block is observed to fall \(76.5 \mathrm{~cm}\) in \(5.11\) s. Calculate the rotational inertia of the pulley.
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Dynamics

Read Explanation

Turning Points in Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Rotational Dynamics

Read Explanation

Engineering Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free