Cantidades Rotacionales Básicas

The angular displancment is defined by: For a circular path it follows that the angular velocity is and the angular acceleration is where the acceleration here is the tangential acceleration.

Angular Velocity

Vector angular velocity

For an object rotating about an axis, every point on the object on the object has the same angular velocity. The tangential velocity of any point is proportional to its distance from the axis of rotation. Angular velocity has the units rad/s. Angular velocity is the rate of change of angular displacement and can be described by the relationship and if v is constant, the angle can be calculated from

Description of Rotation

Rotation is described in terms of angular displacement , time , angular velocity , and angular acceleration . Angular velocity is the rate of change of angular displacement and angular acceleration is the rate of change of angular velocity. The averages of velocity and acceleration are defined by the relationships:

where the Greek letter delta indicates the change in the quantity following it.

A bar above any quantity indicates the average value of that quantity. If a is constant, equations 1,2, and 3 represent a complete description of the rotation. Equation 4 is obtained by a combination of the others.

Rotation Equations

Comments on Rotation Calculation

In the example rotation calculation, some assumptions are made about the calculation order. The rotation equations represent a complete set of equations for constant angular acceleration rotations, but in certain types of problems, intermediate results must be calculated before proceeding to the final calculation. In the example calculation, you may have to do intermediate calculations, e.g., to establish the final angular velocity, in order to set up the problem you wish to solve, just as if you were working the problem with calculator and paper. In the example calculation, the time, initial angular velocity, and displacement were considered given (primary) unless they were being calculated (e.g., in calculating a). If u is being calculated, then v is assumed given, so it must be calculated first if you want to specify a. If initial angular velocity is being calculated, then v is presumed given. If time is being calculated then a is presumed given.