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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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Most popular questions from this chapter

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10revs;60revolutions later, its angular speed is 15鈥�revs.

Calculate

(a) the angular acceleration,

(b) the time required to complete the 60 revolutions,

(c) the time required to reach the 10鈥�revsangular speed, and

(d) the number of revolutions from rest until the time the disk reaches the 10鈥�revs angular speed

In Fig. 10 - 37, two particles, each with mass m = 0.85KG , are fastened to each other, and to a rotation axis at O , by two thin rods, each with length d = 5.6cm and mass M = 1.2kg . The combination rotates around the rotation axis with the angular speed v = 0.30rad/s . Measured about O, what are the combination鈥檚 (a) rotational inertia and (b) kinetic energy?

Figure 10 - 27shows three flat disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk consists of the same two materials, one denser than the other (density is mass per unit volume). In disks 1and 3, the denser material forms the outer half of the disk area. In disk 2, it forms the inner half of the disk area. Forces with identical magnitudes are applied tangentially to the disk, either at the outer edge or at the interface of the two materials, as shown. Rank the disks according to (a) the torque about the disk center, (b) the rotational inertia about the disk center, and (c) the angular acceleration of the disk, greatest first.

A 32.0鈥塳驳wheel, essentially a thin hoop with radius1.20鈥尘, is rotating at280鈥塺别惫/min. It must be brought to a stop in15.0鈥塻. (a) How much work must be done to stop it? (b) What is the required average power?

The angular position of a point on the rim of a rotating wheel is given by, 胃=4.0t-3.0t2+t3where 胃 is in radians and t is in seconds. What are the angular velocities at

(a) t=2.0sand

(b) t=4.0s?

(c) What is the average angular acceleration for the time interval that begins at t=2.0sand ends at t=4.0s? What are the instantaneous angular accelerations at

(d) the beginning and

(e) the end of this time interval?
See all solutions

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