A body of radius R and mass m is rolling horizontally without slipping with a unifrom speed v. It then rolls up in an inclined plane to a maximum height of h. If h =`(3v^2)/(4g)`, determine the MI of the body about its axis of rotation.

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by v^2=(2gh)/ (i+k^2^l R^3 Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

If a body is moving in a circle of radius r with a constant speed v m/s. Its angular velocity is

A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so.that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?

A simple pendulum of length I and mass m is suspended in a car that is travelling with a constant speed v around a circle of radius R. If the pendulum undergoes small oscillations about its equilibrium position, what will be its frequency•of oscillation ?

A solid cylinder rolles down an inclined plane. Its mass is 2 kg and radius 0.1 m. If the height of the inclined plane is 4m, what is its rotational kinetic energy when it reaches the bottom.

Obtain an expression for the centripetal force required to make a body of mass m moving with a constant speed v around a circular path of radius r.

A disc rotating about its axis with angular speed ?Qis placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated?

MI of a thin circular disc about an axis passing through its centre and perpendicular to its plane is 1/2 MR^2 , where M is the mass of the disc and R is its radius. Find an expression for radius of gyratiuon of the disc about an axis tangential to the edge and peerpendicular to the plane of rotation.

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2IS, where M is the mass of the sphere and R is the radius of the sphere(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2I4, find its moment of inertia about an axis normal to the' disc and passing through a point on its edge.

A 70 kg man stands in contact against the inner wail of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to ' remain stuck to the wall (without falling) when the floor is suddenly removed?