#Radians and cancellation

21 messages · Page 1 of 1 (latest)

median dome
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What does this mean?

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merry valleyBOT
median dome
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In the particular video, he said in order for the radian to be cancelled, the theta has to be measured in radians

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So what would be S = ?

low oyster
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can you send the url at that time?

median dome
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9:30

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Oh is it because so that S (the arc length) can be equal to the radius?

low oyster
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we need both sides of the equation to have the same unit

median dome
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both sides of the equation to have the same unit?

low oyster
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S and R have a unit of distance so θ must act as a dimensionless quantity. What he does is show that S=rθ/(1 rad). Since S and r have units of distance, θ and 1 rad must have the same unit to cancel out and become dimensionless

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dimensionless as in having no unit

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it is sort of like speed = distance / time. speed has units m/s so distance must have units m and time must have units s

median dome
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I think I get the gist of it now

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Since the Radian acts a relationship as central angle that makes the arc equal to the radius of the circle?

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And for it to be 1 RAD, the arc has to be equal to the radius

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Is this correct?

low oyster
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if the central angle is 1 radian then the arclength is indeed equal to the radius

median dome
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I see

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I think its clear now thanks a lot for the help