Question

What is angular velocity and acceleration in uniform circular motion

Answer 1

Angular velocity

⇒The position of particles of particles P at a Given  instant may be describe by the angle  θ between OP and OX .This angle  θ is called the angular position of the particles . As particles moves on the the circle its angular position  θ changes . suppose the point rotates an angle Δ θ  in Δt . the rate of change of angular position is know as as angular position (ω), thus

$\boxed{\rm \omega= \displaystyle\lim_{\Delta t\to 0} \frac{\Delta \theta}{\Delta t}=\frac{d\theta}{dt} }$

Angular Acceleration

⇒ The rate of change of angular velocity is called Angular Acceleration

$\boxed{\rm\alpha=\dfrac{d\omega}{dt}=\frac{d^2\theta}{dt^2} }$

More about angular acceleration

⇒ angular acceleration is also vector quantity . direction of α is also perpendicular to plane of circle either parallel or antiparallel to ω  if angular speed of particles is increasing then α is parallel to ω