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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.

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Most popular questions from this chapter

Attached to each end of a thin steel rod of length1.20m and mass6.40kg is a small ball of mass1.06kg . The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. At a certain instant, it is rotating at 39.0rev/s. Because of friction, it slows to a stop in32.0s .Assuming a constant retarding torque due to friction, compute

(a) the angular acceleration,

(b) the retarding torque,

(c) the total energy transferred from mechanical energy to thermal energy by friction, and

(d) the number of revolutions rotated during the32.0s .

(e) Now suppose that the retarding torque is known not to be constant. If any of the quantities (a), (b), (c), and (d) can still be computed without additional information, give its value.

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