establish a relationship between linear velocity and angular velocity in a uniform circular motion.what will be the direction of the linear velocity and acceleration at any instant in a uniform circular motion
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As we know ,
linear velocity =displacement /time.
angular velocity =angular displacement /time
Now, let a body is moving in a circular path with radius "r". Due to certain linear displacement "s" an angle will be produced at centre if we draw two radii from initial and final position to centre ,let that is "♡".
From concept of geometry we can write,
♡=s/r
or,♡r=s
If we divide both sides of the equation by time(t),we will obtain ♡r/t=s/t
(♡/t)×r=s/
♡/t=angular velocity
s/t=linear velocity
so, angular velocity ×radius =linear velocity
the direction of linear velocity will be along the tangent drawn at the point on circular path that instant position of the body.
Acceleration will be directed to the centre of that circle.
linear velocity =displacement /time.
angular velocity =angular displacement /time
Now, let a body is moving in a circular path with radius "r". Due to certain linear displacement "s" an angle will be produced at centre if we draw two radii from initial and final position to centre ,let that is "♡".
From concept of geometry we can write,
♡=s/r
or,♡r=s
If we divide both sides of the equation by time(t),we will obtain ♡r/t=s/t
(♡/t)×r=s/
♡/t=angular velocity
s/t=linear velocity
so, angular velocity ×radius =linear velocity
the direction of linear velocity will be along the tangent drawn at the point on circular path that instant position of the body.
Acceleration will be directed to the centre of that circle.
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