/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 76 The sphere of mass M and radius ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q. 76 (page 333)

The sphere of mass M and radius R in FIGURE P12.76 is rigidly attached to a thin rod of radius r that passes through the sphere at distance 12 R from the center. A string wrapped around the rod pulls with tension T. Find an expression for the sphere鈥檚 angular acceleration. The rod鈥檚 moment of inertia is negligible.

Short Answer

Expert verified

The expression for the sphere鈥檚 angular acceleration is 伪=20Tr13MR2

Step by step solution

01

Given information

Mass of sphere = M

Radius of sphere = R
radius of rod = r
Sphere is attached with Rod at R/2 distance from the center of the sphere.
Rod is pulled with a string with tension T
The moment of inertia of the rod is negligible.

02

Explanation

From the parallel axis theorem moment of inertia is given by

I=25MR2+MR22I=MR225+14I=13MR220

Torque on the sphere is calculated by

蟿=Frsin胃

In this case only tension force is applicable so

蟿=Tr............................(2)

Torque is calculated by another way using angular acceleration

蟿=I伪..........................(3)

From equation (2) and (3)

I伪=Tr伪=TrI.......................(4)

Substitute values , we get

伪=Tr13MR220伪=20Tr13MR2

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 1.3kg ball on the end of a lightweight rod is located at (x,y)=(0.3m,2.0m)where the yaxis is vertical. The other end of the rod is attached to a pivot at (x,y)=(0m,3.0m). What is the torque about the pivot? Write your answer using unit vectors.

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel鈥檚 energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. Its maximum angular velocity is 1200 rpm.
a. A motor spins up the flywheel with a constant torque of 50 N m. How long does it take the flywheel to reach top speed?
b. How much energy is stored in the flywheel?

c. The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.0 s. What is the average power delivered to the machine?
d. How much torque does the flywheel exert on the machine?

A 4.0 kg, 36 cm-diameter metal disk, initially at rest, can rotate on an axle along its axis. A steady 5.0 N tangential force is applied to the edge of the disk. What is the disk's angular velocity, in rpm, 4.0 s later?

A ceiling fan with 80 cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25s after being turned off.

A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite鈥檚 speed at point a is 8000 m/s.
a. Does the satellite experience any torque about the center of the planet? Explain.
b. What is the satellite鈥檚 speed at point b?
c. What is the satellite鈥檚 speed at point c?
See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Magnetism

Read Explanation

Physical Quantities And Units

Read Explanation

Quantum Physics

Read Explanation

Electricity

Read Explanation

Scientific Method 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.