Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q11P (page 287)

A disk, initially rotating at 120 rads, is slowed down with a constant angular acceleration of magnitude 120 rads2.

(a) How much time does the disk take to stop?

(b) Through what angle does the disk rotate during that time?

Short Answer

Expert verified
  1. The time required for a disk to come to rest,t=30.0 s
  2. The angular displacement of the disk while it comes to rest,θ=1.8×103rad

Step by step solution

01

Determine the given quantities

The initial angular velocity of the disk,ω0=120 rads

The angular acceleration of the disk,α=−4.0 rads2

02

Determine the concept of kinematic equations

Use the kinematic equation for constant angular acceleration to solve for time and angular displacement.

ω=ω0+αt

θ=ωt−12αt2

03

(a) Calculate the time required by the disk to take stop.

Kinematic equation for angular motion is:

ω=ω0+αtt=ω-ω0α

Substitute the values and solve further as:

t=0−120−4.0=30.0s

The time required for a disk to come to rest, t=30.0 s.

04

(b) Calculate the rotation angle of disk

Consider the formula for the rotation angle as:

θ=ωt−12αt2=0×30.0−12×(−4.0)×30.02=1.8×103 rad

The angular displacement of the disk while it comes to rest,θ=1.8×103rad.

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 uniform cylinder of radius 10cmand mass 20kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0cm from the central longitudinal axis of the cylinder.

(a) What is the rotational inertia of the cylinder about the axis of rotation?

(b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

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

Figure 10-34ashows a disk that can rotate about an axis at a radial distance hfrom the center of the disk. Figure 10-34b gives the rotational inertia lof the disk about the axis as a function of that distance h, from the center out to the edge of the disk. The scale on the laxis is set by lA=0.050kg.m2andlB=0.050kg.m2. What is the mass of the disk?

At t=0, a flywheel has an angular velocity of4.7 rad/s, a constant angular acceleration of−0.25 rad/s2, and a reference line atθ0=0.

(a) Through what maximum angleθmaxwill the reference line turn in the positive direction? What are the

(b) first and

(c) second times the reference line will beθ=12θmax?

At what(d) negative time and

(e) positive times will the reference line be atθ=10.5 rad?

(f) Graphθversust, and indicate your answers.

A bicyclist of mass 70kg puts all his mass on each downward moving pedal as he pedals up a steep road. Take the diameter of the circle in which the pedals rotate to be0.40m , and determine the magnitude of the maximum torque he exerts about the rotation axis of the pedals.
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Waves Physics

Read Explanation

Solid State Physics

Read Explanation

Oscillations

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Atoms and Radioactivity

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