$A$ wheel of radius $30 \ cm$ rotates about its axis and undergoes an angular displacement of $30^\circ$. The linear distance covered by the wheel is .......

Two objects of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their respective angular speeds $\omega_1$ and $\omega_2$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_2$ to that of $m_1$ is:

$A$ particle $P$ moves in a circle of radius $a$ with a constant speed $v$. $C$ is the center of the circle,and $AB$ is a diameter. When the particle passes through point $B$,what is the ratio of its angular velocity with respect to $A$ and $C$ respectively?

$A$ particle is performing $U.C.M.$ along the circumference of a circle of diameter $50 \ cm$ with a frequency of $2 \ Hz$. The acceleration of the particle in $m/s^2$ is:

$A$ stone tied to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolutions in $44$ seconds,what is the magnitude and direction of the acceleration of the stone?

$A$ particle moves along a circular path of radius $r$ with uniform speed $v$. The angle described by a particle in one second is