A particle $A$ moves along a circle of radius $R$. A fixed point $O$ lies on the circumference of th

Question

A particle $A$ moves along a circle of radius $R$. A fixed point $O$ lies on the circumference of the circle. The radius vector $\mathbf{r}$ drawn to $A$ from point $O$ rotates with a constant angular velocity $\omega$. Which of the following statements is/are CORRECT?

Professor PC Thomas Classes · Answer

By the inscribed angle theorem, the angle $\phi$ subtended at the center is twice the angle $	heta$ subtended at the circumference ($O$). Thus, $\phi = 2	heta$. Angular velocity about the center $\omega_c = d\phi/dt = 2(d	heta/dt) = 2\omega$ (D is incorrect). Velocity $v = \omega_c R = 2\omega R = 	ext{const}$ (A is correct). Since $v$ is constant, tangential acceleration $a_t = dv/dt = 0$ (B is incorrect). Total acceleration is purely normal $a_n = v^2/R = (2\omega R)^2/R = 4\omega^2 R$, directed towards the center (C is correct).