In uniform circular motion, the velocity vector and acceleration vector are

$(a)$ Earth can be thought of as a sphere of radius $6400\, km$. Any object (or a person) is performing circular motion around the axis of the earth due to the earth rotation (period $1$ day). What is acceleration of object on the surface of the earth (at equator) towards its centre ? What is it at latitude $(\theta )$ ? How does these accelerations compare with $g=9.8\,m/s^2$ ?

$(b)$ Earth also moves in circular orbit around the sun once every year with an orbital radius of $1.5 \times 10^{11} \,m$. What is the acceleration of the earth (or any object on the surface of the earth) towards the centre of the sun ? How does this acceleration compare with $g=9.8\,m/s^2$ ?

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

A particle is moving in a circle of radius $r$ having centre at $O$, with a constant speed $v$. The magnitude of change in velocity in moving from $A$ to $B$ 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 net applied force on a body in uniform circular motion should always be