A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of $120 \mathrm{cm}$ and $\mathrm{rpm} 1500$ at full speed. Consider a particle of mass $1 \mathrm{g}$ sticking at the outer end of a blade.

(a) How much force does it experience when the fan runs at full speed?

(b) Who exerts this force on the particle?
(c) How much force does the particle exert on the blade along its surface?

A block of mass $m$ is kept on a horizontal ruler. The friction coefficient between the ruler and the block is $\mu$. The ruler is fixed at one end and the block is at a distance $L$ from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end.

(a) What can be the maximum angular speed for which the block does not slip?

(b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration $\alpha$, at what angular speed will the block slip?

There are two blocks of masses $m_1$ and $m_2\text{.} m_1$ is placed on $m_2$ on a table which is rotating with an angular velocity $\omega$ about the vertical axis. The coefficient of friction between the blocks is ${\mu }_1$ and between $m_2$ and table is ${\mu }_2 \left({\mu }_1<{\mu }_2\right)$. If the blocks are placed at a distance $R$ from the axis of rotation for relative sliding between the surfaces in contact, find the,

(a) frictional force at the contacting surface

(b) maximum angular speed $\mathrm{\omega }$.

A block of mass $m_1$ connected with another block of mass $m_2$ by a light spring of natural length $l_0$ and stiffness $k$ is kept stationary on a rough horizontal surface. The coefficient of friction between $m_1$ and surface is $\mu$ and the block $m_2$ is smooth. The block $m_2$ is moved with certain speed so as to execute uniform circular motion around the block $m_1$ in horizontal plane.
Find the (a) maximum angular speed of the block $m_2$ relative to $m_1$ (b) acceleration of $m_2$ in (a).

A small block is connected to one end of two identical massless strings of length $16\frac{2}{3} \mathrm{cm}$ each with their other ends fixed to a vertical rod. If the ratio of tensions $\frac{T_1}{T_2}$ be $4:1$, then what will be the angular velocity $\omega$ of the block?

Two wires $AC$ and $BC$ are tied at $C$ of small sphere of mass $5 \mathrm{kg}$ which revolves at a constant speed $v$ in the horizontal circle of radius $1.6 \mathrm{m}$. Find the minimum value of $v$.