Educator

Rotation of a Rigid Body About a Fixed Axis

• When a particle rotates in a circle, its linear speed is equal to the product of the angular speed and the radius.
• For a rotating rigid body, at any given instant, every part of the body rotates with the same angular speed, but different parts may have different linear speeds.
• For constant angular acceleration, we may write simple equations that connect the angular displacement, angular velocity, angular acceleration, and time.
• The kinetic energy of a rotating rigid body is given by Iw²/2, where I is the moment of inertia of the rigid body, and w is its angular velocity.
• The moment of inertia of a rigid body depends on its mass and shape. For highly symmetric objects such as rods, rings, disks, cylinders, and spheres, simple formulas for the moment of inertia may be easily obtained.