How to find angular acceleration

How to find angular acceleration

Angular acceleration is a pseudo-vector physical quantity which characterizes speed of change of angular speed. Thus, angular acceleration characterizes rotary movements of a solid body whereas linear acceleration - its progress. As linear acceleration of a body is connected with its speed, and its angular acceleration is connected with its angular speed. Between angular and linear acceleration there is also a communication.

It is required to you

  • angular speed, tangential acceleration


1. Follows from definition of angular acceleration that for its calculation it is necessary to know angular speed. The vector of angular speed on the module is equal to a body angle of rotation in unit of time: v = df/dt where v is angular speed, df is an angle of rotation. The vector of angular speed will be sent by the rule of the gimlet on a rotation axis, that is to that party in which the gimlet with the right carving would be screwed in if rotated in the same party.

2. As angular acceleration characterizes speed of change of angular speed, by definition, it is equal on the module: = dv/dt = (d^2) of f/d(t^2). Thus, angular acceleration in this sense similarly linear, only the second derivative on time undertakes from angular speed, but not linear.

3. Let's find the directions of a vector of angular acceleration now. Obviously, it will be directed on a rotation axis. If the size of a vector is more than zero, that is the body will accelerate, then the vector of a will be sent to the same party, as a vector of angular speed. If size a is negative and the body slows down, then the vector will be sent to the opposite direction.

4. Angular acceleration can also be expressed on a formula: = At/R. In this formula At - tangential acceleration, and R - the radius of curvature of a trajectory. Tangential acceleration is a component of full linear acceleration, directed on a tangent to a trajectory of the movement. You should not confuse it with normal (or centripetal) acceleration which is directed to the center of curvature of a trajectory.

Author: «MirrorInfo» Dream Team