Chapter 10, Problem 062 Your answer is partially correct. Try again. In the figu

Question

Chapter 10, Problem 062 Your answer is partially correct. Try again. In the figure, three 0.03 kg particles have been glued to a rod of length L = 11 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to 20.0 rad/s, (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly's kinetic energy (in joules) versus the square of its rotation rate (in radians-squared per second-squared)? Axis 0 UnitsTj (a) Number1.016 (b) Number 3.049 (c) NumberT-3.812 (d) Number o.00254:1 UnitsTj Un UnitsT kg.m 2

Explanation / Answer

a)

Total Moment of inertia

ITotal = mL2 +m(2L)2+m(3L)2=14m(L/3)2

Work done

W=(1/2)IWf2-(1/2)IWi2

W=(1/2)*(14*0.03*(0.11/3)2)(202-02)

W=0.113 J

b)

W=(1/2)*(14*0.03*(0.11/3)2)(202-02)

W=0.3388 J

c)

W=(1/2)*(14*0.03*(0.11/3)2)(602-402)

W=0.5647 J

d)

Slope=7m(L/3)2=7*0.03*(0.11/3)2 =2.8233*10-4 Kg-m2

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