A solid sphere of mass 0.5 kg and diameter 1 m rolls without sliding with a constant velocity of 5 m/s, the ratio of the rotational K.E. to the total kinetic energy of the sphere is :

Analogue of mass in rotational motion is

Newton's second law of motion and work done in rotation of a rigid body can be expressed as 

How do you express Newton's second law of motion in differential form

If Kinetic energy is expressed as $mv^2/2$ for a particle undergoing uniform velocity motion, How is the kinetic energy expressed in case of the same particle, if it was rotating:

A sphere rolls down on an inclined plane of inclination $\theta$. What is the acceleration as the sphere reaches bottom?

What is the displacement of the point on the wheel initially in contact with the ground when the wheel rolls forwards half of revolution? Take the radius of the wheel as $'R'$ and the x-axis in the forward direction

A solid cylinder rolls down a rough inclined plane without slipping. As it goes down, what will happen due to force of friction?

A ball rolling off the top of a staicase of each step with height H and width W, with an initial velocity U will just hit nth step. Then n = 

A small charged ball of mass m and charge q is suspended from the highers point of a ring of radius R by means of an insulated code of negligible mass.The ring is made of a rigid wire of negligible cross-section and lies in a vertical plane.On the ring, there is uniformly distributed charge Q of the same as that of q .determine the length of the cord so as the equilibrium position of the ball lies on the symmetry axis ,perpendicular to the plane of the ring. 

If a spherical ball rolls on a table without slipping the fraction of its total energy associated with rotation is:

A coin placed on a rotating turn table just slips if it is at a distance of $40$ cm from the centre if the angular velocity of the turntable is doubled, it will just slip at a distance of 

The minimum coefficient of friction for which the sphere will have pure rolling after some time, for $\theta ={ 45 }^{ 0 }$ is

A wheel whose radius is $r$ and moment of inertia about its-own axis is $I$, can rotate freely about its own horizontal axis. A rope is wrapped on the wheel. A boy of mass $m$ is suspended from the free end of the rope. The body is released from rest. The velocity of the body after falling a distance $h$ would be- 

A solid cylinder (SC),Hollow cylinder (HC)& solid sphere (SS)of same mass & radii are released simultaneously from the same height on an incline. The order in which they will reach the bottom is (From least time to most time order)

A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt moving horizontally with an increasing velocity $v=a+{ bt }^{ 2 }$. If the cylinder is not allowed to slip then the time when the cylinder is about to topple, will be equal to

A solid cylinder of mass 2 kg rolls down an inclined plane from a height of 4 cm. Its rotational kinetic energy when it reaches the foot of the plane is (g = 10 ${ m/s }^{ 2 })$

A disc of radius R rolls on a horizontal surface with linear velocity $ \overrightarrow {v} = v \hat {i} $ and angular velocity $ \overrightarrow {\omega} = - \omega \hat k $ there is a particle P on the circumference of the disc which has velocity in vertical direction. the height of that particle from the ground will be

A wheel of mass M and radius a and M.I. $I _G$ (about centre of mass) is set rolling with angular velocity $\omega$ up a rough inclined plane of inclination $\theta$. The distance travelled by it up the plane is :

A disc of mass $m$ of radius $r$ is placed on a rough horizontal surface. A cue of mass $m$ hits the disc at a height $h$ from the axis passing through centre and parallel to the surface. The cue stop and falls down after impact. The disc starts pure rolling for

A uniform rigid rod has length $L$ and mass $m$. It lies on a horizontal smooth surface, and is rotated at a uniform angular velocity $\omega$ about a vertical axle passing through one of its ends. The force exerted by the axle on the rod will be

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

A body is given translational velocity and kept on a surface that has sufficient friction. Then:

(a) A child stands at the center of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of $40$ rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to $2/5$ times the initial value? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?