Rotational Kinematics, Angular Momentum, and Energy

The angle of rotation is a measurement of the amount (the angle) that a figure is rotated about a fixed point— often the center of a circle.

Angular velocity ω is the rate of change of an angle, mathematically defined as ω = $\Delta \theta$$/\Delta t$ .

Angular acceleration is the rate of change of angular velocity, expressed mathematically as $\alpha = \Delta \omega/\Delta t$ .

Constant angular acceleration describes the relationships among angular velocity, angle of rotation, and time.

The motion of rolling without slipping can be broken down into rotational and translational motion.

Rotational inertia is the tendency of a rotating object to remain rotating unless a torque is applied to it.

The rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.

The moment of inertia is a property of a mass that measures its resistance to rotational acceleration about one or more axes.

The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.

In a closed system, angular momentum is conserved in a similar fashion as linear momentum.

The direction of angular quantities, such as angular velocity and angular momentum, is determined by using the right hand rule.

A gyroscope is a spinning wheel or disk in which the axle is free to assume any orientation.

Identify the problem and solve the appropriate equation or equations for the quantity to be determined.

The description of motion could be sometimes easier with angular quantities such as angular velocity, rotational inertia, torque, etc.

Energy is conserved in rotational motion just as in translational motion.