Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q50P (page 290)

If a 32.0Nmtorque on a wheel causes angular acceleration 25.0rad/s2, what is the wheel’s rotational inertia?

Short Answer

Expert verified

Rotational inertia of the wheel is 1.28kg.m2 .

Step by step solution

01

Understanding the given information

The torque is, τ=32N.m.

The acceleration is, α=25.0rad/s2.

02

Concept and formula used in the given question

You know the torque is nothing but the product of moment of inertia and angular acceleration. This is given by Newton’s second law for rotation. When a wheel is rotating in a direction, it may have its own angular acceleration as well as inertia. From this, you can calculate torque applied on a wheel. In this problem, the torque is given but inertia has to be calculated. The formulas are stated below.

τ=lα

03

Calculation for the wheel’s rotational inertia

Calculating rotational inertia of wheel by using above formula,

τ=lαl=τα

Substitute all the value in the above equation

l=32N.m25.0rad/s2=1.28kg.m2

Hence the rotational inertia is, 1.28kg.m2 .

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

A disk, with a radius of0.25 m , is to be rotated like a merrygo-round through , starting from rest, gaining angular speed at the constant rate α1through the first400 rad and then losing angular speed at the constant rate-α1 until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed400 ms2 .

(a) What is the least time required for the rotation?

(b) What is the corresponding value ofα1 ?

Figure 10-36shows an arrangement of 15identical disks that have been glued together in a rod-like shape of length L = 1.0000M and (total) massM = 100.0mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O . (a) What is the rotational inertia of the arrangement about that axis? (b) If we approximated the arrangement as being a uniform rod of mass Mand length L , what percentage error would we make in using the formula in Table 10-2eto calculate the rotational inertia?

The flywheel of a steam engine runs with a constant angular velocity of . When steam is shut off, the friction of the bearings and of the air stops the wheel in 2.2 h.

(a) What is the constant angular acceleration, in revolutions per minute-squared, of the wheel during the slowdown?

(b) How many revolutions does the wheel make before stopping?

(c) At the instant the flywheel is turning at75revmin , what is the tangential component of the linear acceleration of a flywheel particle that is50 cm from the axis of rotation?

(d) What is the magnitude of the net linear acceleration of the particle in (c)?

In Fig.10−41 , block 1has mass m1=460 g, block 2has massm2=500 g , and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R=5.00 cm. When released from rest, block 2 falls75.0 cm in5.00 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tensionT2 and (c) tensionT1 ? (d) What is the magnitude of the pulley’s angular acceleration? (e) What is its rotational inertia?

Figure 10−43 shows a uniform disk that can rotate around its center like a merry-go-round. The disk has a radius of 2.00 cm and a mass of  20.0 gramsand is initially at rest. Starting at time t=0, two forces are to be applied tangentially to the rim as indicated, so that at time t=1.25 sthe disk has an angular velocity of250 rad/s counterclockwise. Force F→1has a magnitude of0.100 N . What is magnitudeF→2 ?
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Atoms and Radioactivity

Read Explanation

Fundamentals of Physics

Read Explanation

Waves Physics

Read Explanation

Electromagnetism

Read Explanation

Energy 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