Question

define uniform circular motion. for uniform circular motion, prove that linear velocity v=r*omega.

Answer 1

UNIFORM CIRCULAR MOTION :

⏺️When an object is moving on the circular path with constant speed, then it is said to be UNIFORM CIRCULAR MOTION.

✔️PROVING :

Angular Displacement in time Δt is given by

Δθ =Δ s / r

Divide by Δt,

Δθ / Δt = ( Δ s / Δ t ) * ( 1 / r)

If Δ t --> 0, ( If Δ t tends to 0 )

d θ / dr = ( ds / dt ) * ( 1 / r)

ω = v / r

✔️ v = r ω

Answer 2

AS VELOCITY = DISPLACEMENT/ TIME

AS DISPLACEMENT = ARC LENGTH WHEN LENGTH IS SMALL
AS ARC LENGTH = THETA × RADIUS

SO THETA × radius/ time

AS THETA/ TIME = omega

so v= rw