"Relation between linear velocity and angular velocity"
please explain.
Answers
Let us consider a body P moving along the circumference of a circle of radius r with linear velocity v and angular velocity ω as shown in Fig.. Let it move from P to Q in time dt and dθ be the angle swept by the radius vector.
Let PQ = ds, be the arc length covered by the particle moving along the circle, then the angular displacement d θ is expressed as dθ = ds/r. But ds=vdt.
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Heya.....!!!
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Given in the question :-
( v ) => Linear Velocity .
( ω ) => Angular Velocity .
There is a realtion between linear displacement and angular displacement .
let angular displacement be ( x )
Angle which is moved by particle ( θ )
radius ( r )
=> θ = x / r
=> x = r θ .............( i )
in this equation ( i ) divide both side by ( t ) time
=> x / t = rθ/t
=> x / t. = v ,, θ/t. = ω
v = rω
Hence the realtion between angular velocity and linear velocity is