Radians vs Degrees

2 Key excerpts on "Radians vs Degrees"

• 

  eBook - ePub

  Mechanical Design for the Stage

  • Alan Hendrickson(Author)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  Figure 7.2 ). Regardless of the units used to measure the radius and arc length—feet, meters, or light years—the ratio cancels those units out and the result is a dimensionless number. So, for instance, angular speed will be described in terms of “radians per second” to unambiguously state how the angles are measured, but the true units of angular speed are simply “per second” or “1/sec”.

  Figure 7.2 Radian angle measurement

  One full revolution, or 360°, in radian measure is the ratio of the circumference of a circle of radius r to that radius, r. Since the circumference is 2πr, the ratio of arc length to radius for one revolution becomes (see right side of Figure 7.2 )

  This value allows two common conversions to be developed—degrees to radians

  d e g r e e s ×

  2 π   r a d i a n s   p e r   r e v o l u t i o n

  360   d e g r e e s   p e r   r e v o l u t i o n

  = d e g r e e s × 0.075 = r a d i a n s

  t u r n s × 2 π = t u r n s × 6.28 = r a d i a n s

  EXAMPLE: During a scene change, a turntable rotates 110° (the direction of rotation is intentionally being left out, for reasons to be explained below). What is its angular displacement in radians?

  SOLUTION: Since displacement is the subtraction of one position from another, or, stated differently, the difference between two positions, the exact value of the initial position at time t1

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  eBook - ePub

  Construction Mathematics

  • Surinder Virdi, Roy Baker, Narinder Kaur Virdi(Authors)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  CHAPTER 10

  Geometry

  Learning outcomes: (a) Identify the different types of angles, triangles and quadrilaterals (b) Find angles in triangles, quadrilaterals and other geometrical constructions (c) Use Pythagoras’ theorem to determine diagonals in quadrilaterals and sides of right-angled triangles (d) Calculate the circumference of a circle

  10.1 Angles

  When two straight lines meet at a point an angle is formed, as shown in Figure 10.1 . There are two ways in which an angle can be denoted, i.e. either ∠CAB or ∠A .

  Figure 10.1

  The size of an angle depends on the amount of rotation between two straight lines, as illustrated in Figure 10.2 . Angles are usually measured in degrees, but they can also be measured in radians. A degree, defined as of a complete revolution, is easier to understand and use as compared to the radian. Figure 10.2 shows that the rotation of line AB makes (a) revolution or 90 , (b) revolution or 180 , (c) revolution or270° and (d) a complete revolution or 360°.

  Figure 10.2

  For accurate measurement of an angle a degree is further divided into minutes and seconds. There are 60 minutes in a degree and 60 seconds in a minute. This method is known as the sexagesimal system: 60 minutes (60′) = 1 degree 60 seconds (60″) = 1 minute (1′) The radian is also used as a unit for measuring angles. The following conversion factors may be used to convert degrees into radians and vice versa. 1 radian = 57.30° (correct to 2 d.p.) π radians = 180° (π = 3.14159; correct to 5 d.p.) 2π radians = 360° Example 10.1 Convert: (a) 20°15′25″ into degrees (decimal measure) (b) 32.66° into degrees, minutes and seconds. (c) 60°25′45″ into radians.

  Solution:

  (a) The conversion of 15′25″ into degree involves two steps. The first step is to change 15′25″ into seconds, and the second to convert seconds into a degree. This is added to 20° to get the final answer.

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