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A particle moves along a circle of radius R with a constant angular speed omega. Its displacement(only magnitude)in time t will be

A particle moves along a circle of radius R with a constant angular speed omega. Its displacement(only magnitude)in time t will be

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1 Answers

Susmita
425 Points
5 years ago
Draw a circle.Draw two points A,B on its perimeter.Join A and B by a straight line.Say the length of it is x.We have to find out x.
Join A and B with centre of the circle 0.These two lines AO and BO are basically two radius.So each has a length of R.
Angular speed
\omega = \frac{d \theta}{dt}
Or,theta=omega×t
theta is angle A0B.
Now draw a perpendicular bisector on AB from O.It will divide AB in two segments of length x/2 and divide the angle theta into two equal angle theta/2.
From any of the triangle
sin(theta/2)=(x/2)/R
Or,x=2Rsin(theta/2)=2Rsin(omega×t/2)
Please approve the answer in you are helped.

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