The acceleration vector of a particle in uniform circular motion averaged over the cycle is a null vector. This statement is

The angular speed of earth around its own axis is ......... $rad / s$

The linear speed of the tip of seconds hand of a wall clock is $1.05\,cm\,s^{-1}.$ The length of the seconds hand is nearly  ........ $cm$

Three point particles $P, Q, R$ move in circle of radius $‘r’$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in rad/ sec) of $P, Q$ and $R$ are $5\pi , 2\pi$ & $3\pi$ respectively, in the same sense. The time interval after which they are at same angular position.

A simple pendulum consisting of a mass $M$ attached to a string of length $L$ is released from rest at an angle $\alpha$. $A$ pin is located at a distance $l$ below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle $\theta$ which string makes with the vertical after hitting the pin is :-

An aeroplane is flying with a uniform speed of $100\, m/s$ along a circular path of radius $100 m$. the angular speed of the aeroplane will be ......... $rad/sec$