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Chapter 10: Q36P (page 288)

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?

Short Answer

Expert verified

The mass of the disk is, 2.5kg

Step by step solution

01

Understanding the given information

  1. Moment of inertia at hA=0mis lA=0.050kg.m2
  2. Moment of inertia at hB=0.2mis, lB=0.150kg.m2.
02

Concept and Formula used in the given question

By applying the parallel axis theorem for two values of moment of inertia as given in the graph we will get two equations. By solving them we can find mass of the disk.

Parallel axis theorem,

l=lcom+mh2

03

Calculation for the mass of the disk

To calculate mass of the disk we will apply Parallel axis theorem for lA and lB

lA=lcom+mhA2 鈥�(1)

lB=lcom+mhB2 鈥�(2)

lcom is the moment of inertia of the disk about its center of mass.

Subtracting equation (2) from (1)

lB-lA=mhB2-hA2m=lB-lAhB2-hA2

Substitute all the value in the above equation.

We can use the values of hA,hB from the given graph

m=0.150kg.m2-0.050kg.m20.2m2-om2=2.5kg

Hence the mass of the disk is, 2.5kg.

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Most popular questions from this chapter

Figure10-21shows plots of angular position胃versus time t for three cases in which a disk is rotated like a merry-go-round. In each case, the rotation direction changes at a certain angular position胃change. (a) For each case, determine whether胃changeis clockwise or counterclockwise from胃=0, or whether it is at胃=0. For each case, determine (b) whether v is zero before, after, or att=0and (c) whether a is positive, negative or zero.

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