What is the definition of the centre of mass for a system of particles?

The centre of mass is the point that moves as if all the mass of the system were concentrated at that point, and all external forces act on it.

A rigid body in pure rotational motion about a fixed axis has ___ for all particles.

The same angular velocity.

True or False: In a rotating rigid body, all particles have the same linear velocity.

False. In a rotating rigid body, particles have different linear velocities depending on their distance from the axis of rotation.

Fill in the blank: The moment of inertia for a thin circular ring about its center is ___.

MR².

What physical quantity is represented by the equation τ = Iα?

Torque, which is the product of the moment of inertia (I) and angular acceleration (α).

Riddle: I am a measure of an object's resistance to change in its rotational motion, and I depend on mass distribution. What am I?

Moment of inertia.

What happens to the angular momentum of a system when no external torque acts on it?

The angular momentum remains constant.

In the context of rotational dynamics, what is the physical significance of the moment of inertia?

It quantifies how mass is distributed with respect to the axis of rotation, affecting how easily the body can be rotated.

Which of the following statements is correct? A) Torque is a scalar quantity. B) Angular momentum can change if there is an external torque. C) Both are true. D) Neither is true.

B) Angular momentum can change if there is an external torque.

What is the relationship between angular displacement θ and linear displacement s for a particle in rotational motion?

S = rθ, where r is the radius of the circular path.

Fill in the blank: The work done by torque τ when the body rotates through an angle θ is given by ___.

W = τθ.

Riddle: I can help you lift heavy loads with less effort, and I am a simple machine. What am I?

A lever.

When a child on a spinning chair pulls their arms in, their angular speed ___ due to the conservation of angular momentum.

Increases.