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Chapter 10: Q11P (page 287)

A disk, initially rotating at 120鈥�rads, is slowed down with a constant angular acceleration of magnitude 120鈥�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鈥塻
  2. The angular displacement of the disk while it comes to rest,胃=1.8脳103rad

Step by step solution

01

Determine the given quantities

The initial angular velocity of the disk,蝇0=120鈥�rads

The angular acceleration of the disk,伪=鈭�4.0鈥�rads2

02

Determine the concept of kinematic equations

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

蝇=蝇0+伪迟

胃=蝇t鈭�12伪迟2

03

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

Kinematic equation for angular motion is:

蝇=蝇0+伪迟t=蝇-蝇0伪

Substitute the values and solve further as:

t=0鈭�120鈭�4.0=30.0s

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

04

(b) Calculate the rotation angle of disk

Consider the formula for the rotation angle as:

胃=蝇t鈭�12伪迟2=0脳30.0鈭�12脳(鈭�4.0)脳30.02=1.8脳103鈥塺补诲

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

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