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 Form 4 Physics uniform circular motion online lessons

Definition of a radian with worked example

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Answer Text:
The radian
-One radian is the angle subtended at the centre of the circle by an arc of length equal to the radius of the
circle.
-Since one circle = #360^0#and has 2 π radians therefore 1 radian = #360^0 / 2#= π r= #57.296^0# or #57.3^0#.
Example
A wheel of radius 50 cm is rolled through a quarter turn.
Calculate
(i) The angle rotated in radians
(ii) The distance moved by a point on the circumference.
Solution
(i) A quarter turn = #360^0 / 4= 90^0. Since 360^0 = 2 pi #radians.
Alternately since 1 radian = #57.3^0 hence 90^0 = 1.57 radii.#
(ii) A point on the circumference moves through an arc,
Arc = radius ×θ (θ in radians) = 50 cm × 1.57 = 78.5 cm.


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