Question

define uniform circular motion show that linear speed of particle performing circular motion is the product of radius of circle and angular speed of particle

Answer 1

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• Derivation. :-»

Let :

( 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 :-


➡ v = r × ω


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