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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

Circular Motion Radius Area

Consider a particle in circular motion as shown in the figure. The position vector sweeps equal area in equal time. Select correct option(s).


(A) the speed is constant
(B) acceleration is constant
(C) $\left| {\overrightarrow {{a_r}} } \right|$ = constant
(D) $a_t = 0$

Let $d\theta$ be the angle swept by the radius in time dt.

Area swept $dA = \frac{1}{2}{r^2}d\theta $

$\frac{{dA}}{{dt}} = \frac{1}{2}{r^2}\frac{{d\theta }}{{dt}} = \frac{1}{2}{r^2}\omega $ where $\omega$ is the instantaneous angular speed.

$\frac{1}{2}{r^2}\omega $ = constant

$\therefore \omega$ = constant or speed v = constant

If speed is constant, $a_t = 0$

${a_r} = \frac{{{v^2}}}{r}$ = constant (magnitude)

The direction of acceleration vector is changing and hence it is not a constant.

(A), (C), (D).