System of Particles and Rotational Motion
The vector relation between linear velocity ($\vec{v}$), angular velocity ($\vec{\omega}$), and position vector ($\vec{r}$) for a rotating particle is:
What is the rotational analogue of force in linear motion?
The moment of inertia of a uniform thin rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to its length is:
If no external torque acts on a rotating system, which of the following physical quantities remains constant?
The moment of inertia of a solid sphere of mass $M$ and radius $R$ about its diameter is:
A ballerina stretches her hands out while spinning and then pulls them closer to her body. What happens to her angular velocity when she pulls her hands in?
The relation between torque $\tau$, moment of inertia $I$, and angular acceleration $\alpha$ is:
The moment of inertia of a circular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:
For a rigid body executing pure rolling motion on a stationary flat surface without slipping, the linear velocity of the point of contact with the ground is:
A solid cylinder and a hollow cylinder of same mass and outer radius roll down an inclined plane from the same height without slipping. Which one reaches the bottom first?
Two particles of masses $1\text{ kg}$ and $3\text{ kg}$ are located at positions $(0,0)$ and $(4,0)\text{ m}$ respectively. The $x$-coordinate of their center of mass is: