An object is moving in a circle of radius $100 \,m$ with a constant speed of $31.4 \,m/s$. What is its average speed for one complete revolution ......... $m/s$

A scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$

A small block slides down from rest at point $A$ on the surface of a smooth cylinder, as shown. At point $B$, the block falls off (leaves) the cylinder. The equation relating the angles $\theta_1$ and $\theta_2$ is given by

If a particle moves in a circle describing equal angles in equal times, its velocity vector

A wheel is rotating at $900\, r.p.m.$ about its axis. When the power is cut-off, it comes to  rest in $1\,minute$ . The angular retardation in $radian/s^2$ is:-

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