Question

Define angular velocity . derive v=rw

Answer 1

Answer:

angular velocity=w. linear velocity=v. v=lenth of the arc/time. w=angular displacement/time. l=r*angular displacement in radians

Explanation:

Answer 2

Answer:

Angular velocity :- The rate of change of angular displacement of a particle is called angular velocity. ${\boxed{\omega = \frac{d\theta}{dt}}}$

Explanation:

Derivation of v = rω :-

• Let us consider a particle moving on circumference pf a circle of radius r.
• Particle moves from A to B the radius ($\overrightarrow{r}$) displaces ᐃѲ in ᐃt time from OA to OB

ᐃѲ = length of arc/radius = AB/r => AB = rᐃѲ

Linear velocity of the particle,

$\displaystyle v = Lim_{\Delta t \to 0}\bigg(\frac{AB}{\Delta t}\bigg) = Lim_{\Delta t \to 0}\bigg(\frac{r\Delta\theta}{\Delta t}\bigg)$

$\displaystyle v = r \:Lim_{\Delta t \to 0}\bigg(\frac{\Delta\theta}{\Delta t}\bigg) = r = \frac{d\theta}{dt}\:\:\:{\boxed{v = r\omega}}\:\:\:\bigg[ \because \:\omega = \frac{d\theta}{dt} \bigg]$