A car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$ . The angular acceleration of the wheel is ........ $rad/s^2$

A fly wheel is accelerated uniformly from rest and rotates through $5 \,rad$ in the first second. The angle rotated by the fly wheel in the next second, will be.........$rad$

A particle moves along a circle of radius $\left( {\frac{{20}}{\pi }} \right)\,m$ with constant tangential acceleration. If the velocity of the particle is $80 \,m/s$ at the end of the second revolution after motion has begin, the tangential acceleration is

An aircraft executes a horizontal loop of radius $1.00\; km$ with a steady speed of $900 \;km/h$. Compare its centripetal acceleration with the acceleration due to gravity.

The angular speed of seconds needle in a mechanical watch is

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 :-