Question

How is the linear speed of a particle moving along a circular path related to its angular velocity???

Answer 1

Heya......!!!!

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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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Hope It Helps You ☺

Answer 2

Answer:Hi mate here is your answer___________________________Explanation:

consider a particle moving with uniform circular motion in anticlockwise direction with Centre O and radius R the particle cover an Arc of length ∆t moving from A to B.....Hence the angular displacement is ∆Ø=∆s/rdividing both side by ∆t∆∅/∆t=1∆s/r∆tin the time interval ∆t be Infinitesimally small [∆t=0]thenlim ∆∅/∆t=1/r[lim ∆s/∆t]but lim ∆∅/∆t=w and lim ∆s/∆t=vtherefore w=v/rv=rwplease mark me brainleast and follow me as it take so much concentration to solve this