Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$, respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal acceleration is

For a particle in uniform circular motion, the acceleration $\vec a$ at a point $P(R,\theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x-$ axis)

The angular speed of a fly wheel making $120$ revolutions/minute is

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is

A particle is moving with constant speed $v$ in $x y$ plane as shown in figure. The magnitude of its angular velocity about point $O$ is .........

The angular acceleration of a body, moving along the circumference of a circle, is :