During circular motion about the origin, a particle's position vector sweeps out equal areas in equal intervals of time. Its

Step-by-step solution

The areal velocity of a particle is given by dA dt = 1 2 r^2 . Since the position vector sweeps out equal areas in equal intervals of time, the areal velocity is constant. For circular motion about the origin, the radius r is constant. Therefore, the angular velocity must also be constant. The speed of the particle is v = r . Since both r and are constant, the speed v remains constant. Because the speed is constant, the tangential acceleration is a_t = dv dt = 0 . Since it is zero, it remains constant. The directio