While using equations of circular motion why do we need to express all

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SUMMARY

In circular motion equations, angles must be expressed in radians to ensure accuracy in calculations. The formula for arc length, s = r θ, holds true exclusively when θ is in radians. This is due to the mathematical relationship where the circumference of a circle is defined as 2πr, linking radians directly to the properties of circles. Understanding this relationship is crucial for applying circular motion equations correctly.

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  • Familiarity with radians and degrees
  • Basic knowledge of trigonometric functions
  • Ability to manipulate mathematical equations
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  • Study the relationship between radians and degrees in detail
  • Explore the derivation of the arc length formula s = r θ
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while using equations of circular motion why do we need to express all angles in radians?
 
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[itex]s = r \theta[/itex] (i.e. arc-length equals radius times angle) is only true when the angle is expressed in radians.
In other words, we know that [itex]\pi[/itex] is a special number, such that the circumfrence equals [itex]2 \pi r[/itex] for any circle. And so we use radians to make use of this special number.
 


good..got it thanks
 

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