Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
8
Rotational Motion
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8-1: Angular Quantities
8-2 and 8-3: Constant Angular Acceleration; Rolling
8-4: Torque
8-5 and 8-6: Rotational Dynamics
8-7: Rotational Kinetic Energy
8-8: Angular Momentum
8-9: Angular Quantities as Vectors

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 1
Q

Express the following angles in radians:

  1. 45.045.0 ^\circ,
  2. 60.060.0 ^\circ,
  3. 90.090.0 ^\circ,
  4. 360.0360.0 ^\circ, and
  5. 445445 ^\circ.
Give as numerical values and as fractions of π\pi.
A
  1. 0.785 rad0.785 \textrm{ rad}
  2. 1.05 rad1.05 \textrm{ rad}
  3. 1.57 rad1.57 \textrm{ rad}
  4. 6.28 rad6.28 \textrm{ rad}
  5. 7.77 rad7.77 \textrm{ rad}
Giancoli 7th Edition, Chapter 8, Problem 1 solution video poster
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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. You convert degrees into radians by multiplying by a conversion factor which could be 2π radians for every 360 degrees; you could have also done π radians per 180 degrees— whichever way you like to think about it— either way you will get the same answer. So 45 times 2 over 360 reduces to 1 over 4 times this π and you get π over 4 radians that's the exact answer for the number of radians for 45.0 degrees. Then as a decimal you take π, divide it by 4 and you get 0.785 radians. 60 times 2 over 360 reduces to one-third and that means you have π over 3 radians here in 60 degrees or 1.05 radians. 90 reduces to π over 2 radians. 360 cancels with 360 on the bottom here leaving us with 2π on the top and you have 6.28 radians as a decimal. And 445 times 2 over 360 reduces to 89 over 36 times π radians and carrying out that arithmetic there, you get 7.77 radians.

COMMENTS
By brf15 on Sat, 11/28/2015 - 8:00 AM

GOOD JOB MR DITCHKO!!!!

By moonpen on Sat, 12/12/2015 - 2:39 AM

I thought I would let you know, for some reason you wrote the answer for b) is 1.95 rad, however in the textbook and in your video it is stated the answer is 1.05 rad.

By Mr. Dychko on Sat, 12/12/2015 - 4:27 AM

Hi moopen, thanks for letting me know about this typo. The '9' is right beside the '0' so that must be why I accidentally entered 1.95 instead of 1.05.

All the best,
Mr. Dychko

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