A couple produces a:

A cylindrical solid of mass M has raidus R and length L. Its moment of inertia about a generator is:

A man of mass M is standing at the centre of a rotating turn table rotating with an angular velocity w. The man holds two 'dumb bells' of mass M/4 each in each of his two hands. If he stretches his arms to a horizontal position, the turn table acquires a new angular velocity w' where

A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A loaded spring gun of mass M fires a 'shot' of mass m with a velocity \(\vartheta \) at an angle of elevation \(\theta\). The gun is initially at rest on a horizontal frictionless surface. After firing, the centre of mass of the gun-shot system

One end of a thin uniform rod of length L and mass M₁ is riveted to the centre of a uniform circular disc of radius r and mass M₂ so that both are coplanar. The centre of mass of the combinsiion from the centre of the disc is (assume that the point of attachment is at the origin).

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is:

If ice on poles melts, then what is the change in duration of day?

A solid cylinder of mass 20 kg rotates about its axis with angular speed of 100 rad/s. The radius of cylinder is 0.25m. What is KE of rotation of cylinder?

If earth contract to half its radius. What would be the length of the day?

Why do we place handles at maximum possible distance from the hinges in a door

When the earth shrinks, without reducing its mass, what change will be there in the duration of a day?

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

A particle on a rotating disc have initial and final angular position are 6rad, -2rad. In which case, particle undergoes a negative displacement.

A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination \({ 30 }^{ \circ }\). The coefficient of static friction,\({ \mu }_{ s }=0.25\).
If the inclination of the plane is increased, at what value of \(\theta \) does the cylinder begin to skid and not roll perfectly?

How much fraction of the kinetic energy of rolling is purely translational

How much fraction of the kinetic energy of rolling is purely rotational.

The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds.
(i) What is its angular acceleration, assuming the acceleration to be uniform?
(ii) How many revolutions does the engine make during this time?

Since his childhood Sanjay had always seen his mother grinding flour in the grindstone. He had observed that his mother had to do a lot of hand work in order to get flour from wheat. He felt very helpless at that time. As he grew older he thought of an idea to connect an electric motor to the wheel of grindstone .  Now, it become very easy to get flour with help of grindstone and now his mother is very happy and felt proud of his intelligence.
When his mother uses grindstone to get flour, what energy transformation takes place?

A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to \(10\ \pi\ rad{ s }^{ -1 }\). Which of the two will start to roll earlier? The coefficient of kinetic friction is \({ \mu }_{ k }\)= 0.2 ?

Show that a.(b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.