Question

If a particle is performing uniform circular motion with radius R, with angular velocity ⍵, then the magnitude of the acceleration is _____

Answer 1

Step 1: Linear velocity of a particle in a circular motion,

Let R be the radius of the circle in which an object travels and ⍵ be the angular velocity.

Then, the linear velocity of the particle is,

$\nu =R\omega$

Step 2: Calculate the centripetal acceleration,

It is the acceleration of an object traversing a circular path.

The magnitude of the centripetal acceleration of the particle is given by,

$$\begin{gathered} {\alpha }_c=\frac{{\nu }^2}{R} \\ {\alpha }_c=\frac{{\left(R\omega \right)}^2}{R} \\ {\alpha }_c={\omega }^{2}R \end{gathered}$$
Thus, the magnitude of the acceleration is ${\omega }^{2}R$.