System of Particles and Rotational Motion

What is the SI unit of moment of inertia?

A uniform rod of length L and mass M is pivoted at one end. What is its moment of inertia about the pivot?

The center of mass of a system of particles is the point where

A solid sphere and a solid cylinder, both having the same mass and radius, roll down an inclined plane without slipping. Which one reaches the bottom first?

If the angular velocity of a rotating body is doubled, its rotational kinetic energy becomes

A system of particles has total mass M and center of mass at position vector \( \vec{R} \). The velocity of the center of mass is \( \vec{V} \). The total linear momentum of the system is

The torque acting on a body about an axis is zero. Which of the following must be true?

Two particles of masses m and 2m are located at points (0,0) and (3,0) respectively. The center of mass is located at:

A disc of radius R rotates about its axis with angular velocity \( \omega \). A particle of mass m is placed at the rim. What is the angular momentum of the particle about the axis?

A wheel of moment of inertia I is rotating with angular velocity \( \omega_0 \). A constant torque \( \tau \) is applied. The angular velocity after time t is: