A car of mass $m$ moving over a concave bridge of radius $r$. Find the normal reaction acting on the car when it is at the lowest point of the bridge.

A particle of mass $m$ is moving with a constant speed $v$ in a circular path in a smooth horizontal plane (plane of the paper) by a spring force as shown in the figure. If the natural length of the spring is $l_0$ and the stiffness of the spring is $k$, find the elongation of the spring.

Ball A is attached to one end of a rigid massless rod, while an identical ball B is attached to the centre of the rod, as figure illustrates. Each ball has a mass $m=0.50 \mathrm{kg},$ and the length of each half of the rod is $L=0.50 \mathrm{m}.$ This arrangement is held by the empty end and is whirled around in a horizontal circle at a constant rate, so each ball is in uniform circular motion. Ball A travels at a constant speed of $v_A=4.0 \mathrm{m} {\mathrm{s}}^{-1}.$ Find the tension in each half of the rod.

A bead of mass m slides along a curved wire lying on a horizontal surface as shown in figure.

$\left(\mathrm{i}\right)$ If the bead slides at constant speed along the wire, draw the vectors representing the force exerted by the wire on the bead at points $\mathrm{A}, \mathrm{B}, \mathrm{and} \mathrm{C}$.
$\left(\mathrm{ii}\right)$ Now consider the bead in figure speeds up with constant tangential acceleration as it moves towards the right. Draw the vectors representing the force on the bead at points $\mathrm{A}, \mathrm{B}, \mathrm{and} \mathrm{C}$.

A small block is supported by a turn-table. The friction coefficient between block and surface is ${\mu }_s$.
(a) If turn-table rotates at constant angular speed $\omega ,$ what can be the maximum angular speed for which the block does not slip?
(b) If the angular speed is increased uniformly from rest with an angular acceleration $\alpha ,$ at what speed will the block slip?