A wheel of radius with 0.5 m and a moment of inertia of $10 \mathrm{~kg}-\mathrm{m}^2$ is rotating freely at an angular speed of 70 $\mathrm{rev} / \mathrm{min}$. The wheel can be stopped in 5.0 s by pressing a wet cloth against the rim and exerting a radially inward force of 88 N . The coefficient of kinetic friction between the wheel and wet cloth is

A solid cylinder of mass $m$ and radius $R$ rolls down on an inclined plane of height 30 m without slipping. The speed of its centre of mass, when the cylinder reaches the bottom is

[use $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A straight rod of length $L$ is made of a material having mass per unit length $m(x)=\lambda|x|$, where $x$ is measured from the centre of rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod will be $L=1 \mathrm{~m}$ and $\lambda=16 \mathrm{~kg} / \mathrm{m}^2$.

Consider a uniform horizontal solid cylinder of mass 10 kg such that its length is 9 times its radius. Let the radius be 40 cm . Calculate the moment of inertia of the cylinder about a line passing through its edge and perpendicular to its axis.