Two bodies of masses 1 kg and 2 kg are located at (1, 2) and (-1, 3), respectively. Calculate the coordinates of the centre of mass.

Centre of gravity of a body on the earth coincides with its centre of mass for a small object and for a large object, it may not. What is the qualiative meaning of small and large in this regards? For which following two of them coincides, a building, a pond, a lake, a mountain.

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?

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 N m. What is the power required by the engine ? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.

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.
A grinding stone of diameter 4 m revolving at 120 rpm accelerates to 660 rpm in 9s. Calculate the angular acceleration and linear acceleration.

A man stands on a rotating platform with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform in 30 rpm. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90 cm to 20 cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg-m².
Is kinetic energy conserved in the process? If not, from where does the change come about?

Define radius of gyration and give the physical significance of moment of inertia

Establish the relationship between Torque and Moment of Inertia.

Locate the centre of mass of a system of particles of mass m₁ = 1 kg, m₂ = 2 kg and m₃ = 3 kg, situated at the corners of an equilateral triangle of side 1.0 metre.

Point masses m₁ and m₁ are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set in rotation about an axis perpendicular to it. Find the position on this rod through which the axis should pass in order that the work required to set the rod i1rotation with angular velocity ω_o should be minimum.