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Chapter 10: Q4Q (page 286)

Figure 10-22鈥塨is a graph of the angular position of the rotating disk of Fig.10-22鈥塧. Is the angular velocity of the disk positive, negative, or zero at (a)t=1s, (b)t=2s, and (c)t=3s? (d) Is the angular acceleration positive or negative?

Short Answer

Expert verified
  1. Angular velocities of the disk, at pointt=1鈥塻is positive.
  2. Angular velocities of the disk, at pointt=2鈥塻is zero.
  3. Angular velocities of the disk, at pointt=3sis negative.
  4. The angular acceleration is negative.

Step by step solution

01

Step 1: Given data

Graph of angular position vs time.

02

Determining the concept

Find the sign of the slope of the graph which represents the sign of angular velocity. Conclude about the angular acceleration from the nature of the graph.

03

(a) Determining if the angular velocity of the disk is positive, negative, or zero at  t= 1 s

The given graph is an angular position vs time graph, so the slope of the graph is angular velocity.

At point t=1, it is positive because the slope is positive.

04

(b) Determining if the angular velocity of the disk is positive, negative, or zero at t= 2 s 

At point t=2, it is zero because the slope is zero.

05

(c) Determining if the angular velocity of the disk is positive, negative, or zero at t= 3 s

At point t=3, it is negative, because slope is negative.

06

(d) Determining if the angular acceleration is positive or negative

The given fact that the original function is concave down, its second derivative must be negative.

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