Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q. 66 (page 333)

The 2.0 kg, 30-cm-diameter disk in Figure P12.66 is spinning at 300 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 3.0 s?

Short Answer

Expert verified

Friction force must be applied by break to rim is : 1.57 N

Step by step solution

01

Given information

The mass of the disk i= 2 kg
The diameter of the disk i= 30 cm
This means radius = 15 cm = 0.15 m
Time taken to stop the disk is = 3 sec
Initial angular speed is = 300 rpm = 10 π rad/sec

Final speed =0

02

Explanation

Calculate moment of inertia of the disk by

I=MR22.........................(1)

Substitute the values we get

I=(2kg)(0.15m)22=0.0225kg.m2

Find the angular velocity using

ωf = ωi + αt ...................................(2)

So the angular acceleration is

α=ωf-ωit...............................(3)

Substitute the values in equation (3), we get

α=(0rad/s-10πrad/s)3s=-10.47rad/s2

Frictional force can be calculated by

f=Iαr..................................(4)Substitutevalues,f=(0.0225kg.m2)(10.47rad/s2)0.15m=1.57N

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

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’s angular acceleration. The rod’s moment of inertia is negligible.

A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straight down the slope. If the slope were frictionless, the cylinder would slide down the slope without rotating. What minimum coefficient of static
friction is needed for the cylinder to roll down without slipping?

A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity v, then the end of the axle is placed on a support that allows the gyroscope to precess. a. Find an expression for the precession frequency Ω in terms of M, R, v, and g. b. A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?

An 800 g steel plate has the shape of the isosceles triangle shown in FIGURE P12.50. What are the x- and y-coordinates of the center of mass?
Hint: Divide the triangle into vertical strips of width dx, then relate the mass dm of a strip at position x to the values of x and dx.

A 200 g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20 g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a frictionless groove in the surface of the turntable. What is the turntable’s rotation angular velocity when the block reaches the outer edge?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Solid State Physics

Read Explanation

Dynamics

Read Explanation

Fluids

Read Explanation

Energy Physics

Read Explanation

Modern 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