COLLEGE PHYSICS-ACHIEVE AC (1-TERM)
COLLEGE PHYSICS-ACHIEVE AC (1-TERM)
3rd Edition
ISBN: 9781319453916
Author: Freedman
Publisher: MAC HIGHER
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Chapter 8, Problem 100QAP
To determine

Angular speed of the dough when the chef catch the pizza.

Expert Solution & Answer
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Answer to Problem 100QAP

  ωafter=4.298rad/s

Explanation of Solution

Given info:

Weight of pizza crust =

  0.500kg

Initial angular speed of dough before expanding =ωbefore=5.20rad/s

Diameter of pizza before expanding =dbefore=20cm

So, rbefore=10cm

Diameter of pizza after expanding =dafter=22cm

So, rafter=11cm

Formula used:

Angular momentum,

  Lz=Iωz ( Lz= Angular momentum, I= moment of inertia, ωz= angular velocity)

Conservation of angular momentum,

  Lbefore=Lafter

  Ibeforeωbefore=Iafterωafter

Calculation:

Moment of inertia of the dough before the expanding,

  Ibefore=12m(rbefore)2

Angular momentum of the dough before the expanding,

  Lbefore=Ibeforeωbefore

  Lbefore=12m(rbefore)2ωbefore...(1)

Moment of inertia of the dough after the expanding,

  Iafter=12m(rafter)2

Angular momentum of the dough before the expanding,

  Lafter=Iafterωafter

  Lafter=12m(rafter)2ωafter...(2)

According to the Conservation of angular momentum,

  Lbefore=Lafter

  Ibeforeωbefore=Iafterωafter

Substituting (1),(2) expressions,

  12m(rbefore)2ωbefore=12m(rafter)2ωafter

  (rbefore)2ωbefore=(rafter)2ωafter

Substituting the given values, we get

  (10×102m)2(5.2rad/s)=(11×102m)2ωafter

  (100×104m2)(5.2rad/s)=(121×104m2)ωafter

  100(5.2rad/s)=121ωafter

  ωafter=100(5.2rad/s)121

ωafter=4.298rad/s

Conclusion:

Thus, angular speed of the dough, after the expanding is 4.298rad/s.

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Chapter 8 Solutions

COLLEGE PHYSICS-ACHIEVE AC (1-TERM)

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