Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Circular Motion, Exercise 1: Classical Thinking

A body of mass $m$ is tied to a string of length $l$ and whirled in a vertical circle. The velocity of the body at the lowest position is $u$. Then the tension in the string at a position when the string makes an angle $\theta$ with the vertical is

A motorcyclist rides in a horizontal circle along the inner wall of a cylindrical chamber of radius $r$. If the coefficient of friction between the tyres and the wall is $\mu$, the minimum angular speed to prevent him from sliding down is

A particle is moving in a vertical circle (It just completes the circle). If $v_1$ is the velocity of particle at highest point and $v_2$ is the velocity of particle at lowest point, then the relation between $v_1$ and $v_2$ is,

Calculate the angular acceleration of a centrifuge which is accelerated from rest to $350 \mathrm{rps}$ in $220 \mathrm{s}$.

A wheel rotates with constant acceleration of $2.0 \mathrm{rad} {\mathrm{s}}^{-2}$. If the wheel has an initial angular velocity of $4 \mathrm{rad} {\mathrm{s}}^{-1}$, then the number of revolutions it makes in the first ten seconds will be approximately,

A car is moving at a speed of $72 \mathrm{km} {\mathrm{hr}}^{-1}$. The diameter of its wheel is $0.5 \mathrm{m}$. If the wheels are stopped in $20$ rotations applying brakes, then angular retardation produced by the brakes would be,

A particle of mass $2 \mathrm{kg}$ is rotating by means of a string in a vertical circle. The difference in the tensions at the bottom and the top would be,

A particle does uniform circular motion in a horizontal plane. The radius of the circle is $20 \mathrm{cm}$. If the centripetal force $F$ is kept constant but the angular velocity is doubled, the new radius of the path (original radius, $R$) will be,