Question

what is angular velocity? Discuss the relation between linear velocity and angular velocity.​

Answer 1

hey here is your answer...

Angular velocity. -the rate of change of angular position of a rotating body.....

Relation between linear velocity and angular velocity

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.

d θ/dt=v/r

(i.e) Angular velocity ω = v/r or v =ω r

In vector notation,

Vector v = Vector ω x Vector r

Thus, for a given angular velocity ω, the linear velocity v of the particle is directly proportional to the distance of the particle from the centre of the circular path (i.e) for a body in a uniform circular motion, the angular velocity is the same for all points in the body but linear velocity is different for different points of the body.

hope it helps u ✌✌✌

Answer 2

Answer:

Answer:

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

➡ ♦ v = r × ω ♦ .

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