Question

relation between linear velocity and angular velocity?

Answer 1

Relationship Between Linear and Angular Quantities

Figure 7.2: Circular Motionegin{figure}egin{center} leavevmode epsfxsize=4 cm epsfbox{fig7-2.eps}end{center}end{figure}

Consider an object that moves from point P to P' along a circular trajectory of radius r , as shown in Figure 7.2.

Definition: Tangential Speed

The average tangential speed of such an object is defined to be the length of arc, $Delta$s , travelled divided by the time interval, $Delta$t :

$displaystyleoverline{v}_{t}^{}$ = . (11)

The instantaneous tangential speed is obtained by taking $Delta$t to zero:

v t = $displaystylelim_{Delta t o 0}^{}$$displaystyle{Delta sover Delta t}$. (12)

Using the fact that

$displaystyleDelta$s = r$displaystyleDelta$$displaystyle heta$ (13)

we obtain the relationship between the angular velocity of an object in circular motion and its tangential velocity:

vt = r$displaystylelim_{Delta t o 0}^{}$$displaystyle{Delta heta over Delta t}$ = r$displaystyleomega$. (14)

This relation holds for both average and instantaneous speeds.

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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