A particle is moving with constant speed $\sqrt 2\,m/s$ on a circular path of radius $10\,cm$. Find the magnitude of average velocity when it has covered ${\left( {\frac{3}{4}} \right)^{th}}$ circular path

If a particle is moving on a circular path with constant speed, then the angle between the direction of acceleration and its position vector w.r.t. centre of circle will be ............ 

Read each statement below carefully and state, with reasons, if it is true or false :

$(a)$ The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre

$(b)$ The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

$(c)$ The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

A stone tied to the end of a string of $1\, m$ 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 going with constant speed along a uniform helical and spiral path separately as shown in figure

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